{"id":1519,"date":"2022-04-20T05:58:33","date_gmt":"2022-04-20T05:58:33","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1519"},"modified":"2023-02-16T03:30:51","modified_gmt":"2023-02-16T03:30:51","slug":"coordinates-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates","title":{"rendered":"Coordinates"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-9271cce5-47fd-49e4-956c-bfe98479c6fd\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates#0-coordinates-introduction>Coordinates: Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates#1-what-are-coordinates-in-math>What Are Coordinates in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates#5-quadrants-in-a-2d-plane>Quadrants in a 2D plane<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates#10-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates#11-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates#12-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"0-coordinates-introduction\">Coordinates: Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space. You might have seen grids being used in math. What are these grids? These grids help us to plot any point using its coordinates. So, what are coordinates in math? Let us see the meaning of coordinates in math.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates of a point in a 2D plane, also known as cartesian coordinates, are two numbers or sometimes a combination of a letter and a number that tell us the exact location of a specific point on a grid. Here, the grid is known as a coordinate plane.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A coordinate plane has four quadrants and two axes: the X-axis is the horizontal axis and the Y-axis is the vertical axis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"568\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-1.png\" alt=\"Cartesian plane\" class=\"wp-image-14434\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-1.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-1-300x274.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-coordinates-of-the-point\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/coordinate_identify_coordinate_pt.png\" alt=\"Identify the Coordinates of the Point Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Coordinates of the Point Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/mark-the-coordinates\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/coordinate_mark_pts_on_plane_pt.png\" alt=\"Mark the Coordinates Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Mark the Coordinates Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"eplus-wrapper wp-block-heading\" id=\"1-what-are-coordinates-in-math\">What Are Coordinates in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us understand the definition of coordinates in math.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates are a pair of numbers which are used to determine the position of a point or a shape in a 2-dimensional plane.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We define the position of a point on a 2D plane using two numbers, called the x-coordinate and the y-coordinate. The x-coordinate always comes first in the ordered pair followed by the y-coordinate and it determines where the point is in the left\u2013right or horizontal direction, and the y-coordinate determines the position of a point in the vertical, up\u2013down direction.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"2-ordered-pair\">Ordered Pair<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, how do you write coordinates? The Cartesian coordinates of a point are usually written in parentheses and separated by commas, like (x, y). Note that the order matters while writing the coordinates of a point.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The coordinates are written as an \u201cordered pair\u201d as shown below. The letter P is simply the name of the point and is used to distinguish it from others.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"304\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-2.png\" alt=\"Writing coordinates of a point\" class=\"wp-image-14435\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-2-300x147.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us look at examples of coordinates.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1:<\/strong> The point where both the axes intersect is known as the origin.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates of the origin are written as O(0, 0).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"564\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-3.png\" alt=\"Coordinates of origin in cartesian plane\" class=\"wp-image-14436\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-3-300x273.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2: <\/strong>In the figure below, the coordinates of point A are (3,4). It means that the point is 3 units along the x-axis and 4 units up.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"597\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-4.png\" alt=\"Coordinates of a point on a cartesian plane\" class=\"wp-image-14437\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-4-300x289.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 3:<\/strong> Coordinates of a point on X-axis and Y-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For a point lying on the X-axis, the y-coordinate is 0. For a point on the Y-axis, the x-coordinate is 0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"674\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-5.png\" alt=\"Coordinates of points on x-axis and y-axis\" class=\"wp-image-14438\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-5-276x300.png 276w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"3-types-of-coordinates\">Types of Coordinates<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We have two major types of coordinate systems as listed below.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Cartesian Coordinate System<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The cartesian coordinate system helps to represent a point uniquely in the n-dimensional coordinate plane. As stated above, it uses the concept of mutually perpendicular lines known as axes, to denote the coordinates of a point. To locate the position of a point P in a plane using two perpendicular lines, the cartesian plane is commonly used. Points are represented in the form of coordinates P(x, y) in two-dimension with respect to x-axis and y- axis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"623\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-6.png\" alt=\"Cartesian coordinate system\" class=\"wp-image-14441\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-6-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-6-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-6-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-6-120x120.png 120w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Polar Coordinate System<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the polar coordinate system, the origin is considered to be a reference point, called a pole. The position of each point is decided by a distance from the pole and an angle is taken from a reference direction.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we express the coordinates of a point as $(r, \u03b8)$. Simply put, we have two parameters\u2014the angle and the radius.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The coordinate r is the length of the line segment from the point (x,y) to the origin and the coordinate \u03b8 is the angle between the line segment and the positive x-axis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"405\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-7.png\" alt=\"Polar coordinate system\" class=\"wp-image-14442\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-7-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Important Note:<\/strong> From the figure, you can see that $\\frac{y}{r} = sin \\theta$ and $\\frac{x}{r} = cos \\theta$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, we can establish the relationship between the cartesian coordinates and the polar coordinates as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = r$ $cos$ and $y = r$ $sin \\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">OR<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^2 + y^2 = r^2$ and $tan \\theta = \\frac{y}{x}$<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"4-coordinates-on-a-plane-2d\">Coordinates on a Plane (2D)<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A 2D coordinate plane is formed by the intersection of x-axis and y-axis. The two axes intersect at a point O(0, 0) called the origin.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The coordinates indicate the position of a point in the 2D coordinate plane relative to the origin. The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis. The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The coordinates are written as an ordered pair of numbers P(x, y), where P is the name of the point, x refers to the horizontal position and y refers to the vertical position.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, the point P(3, 5) is represented as<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"580\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-8.png\" alt=\"Coordinate points on a cartesian plane\" class=\"wp-image-14443\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-8.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-8-300x281.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"5-quadrants-in-a-2d-plane\">Quadrants in a 2D plane<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are basically 4 quadrants in a 2D plane formed due to the intersection of x-axis and y-axis. They are sometimes named using Roman numerals: I, II, III and IV.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You might wonder if the coordinates rules change based on the quadrants or how they are written in different quadrants. Let\u2019s find out.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"499\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-9.png\" alt=\"Quadrants on a cartesian plane\" class=\"wp-image-14444\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-9.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-9-300x241.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Quadrant 1: It\u2019s the top-right quadrant.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, both the coordinates have positive values. For example, P(3, 5), U(8, 4).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Quadrant 2:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, x-coordinate has negative values and y-coordinate has positive values. For example, P$(-3, 5)$, U$(-8, 4)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Quadrant 3:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, both coordinates have negative values. For example, P$(-3, -5)$, U$(-8, -4)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Quadrant 4:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, x-coordinate has positive values and y-coordinate has negative values. For example, P$(3, -5)$, U$(-8, 4)$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"620\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-10.png\" alt=\"Coordinates of a point on different quadrants\" class=\"wp-image-14445\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-10.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-10-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-10-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-10-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-10-120x120.png 120w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"6-coordinate-in-a-space-3d\">Coordinate in a Space (3D)<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A 3D coordinate system can be used to locate the position of a point in 3D space. A 3D coordinate plane is formed by the intersection of three axes\u2014namely the x-axis, y-axis, and the z-axis, which are perpendicular to each other at the origin.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The z-axis can be visualized as an extension to the 2D coordinate plane. Given that the x- and y-axes are the horizontal and vertical axes on a page, the z-axis can be visualized as coming out of, or going through the page, creating the third dimension.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The position of a point in the 3D coordinate plane is quite similar to that of a point in the 2D coordinate plane, with an added z-coordinate: (x, y, z).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"405\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-11.png\" alt=\"What are the coordinates\" class=\"wp-image-14446\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-11.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-11-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"7-how-to-read-and-plot-coordinates\">How to Read and Plot Coordinates<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates are always written within brackets, with the two numbers separated by a comma (,). Coordinates are ordered pairs of numbers. The first number indicates the point on the x-axis (also known as Abscissa) and the second the point on the y-axis (also known as ordinate).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand how to plot a point on the coordinate plane with an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: Plot $(2,3), (3,-2)$ and $(-3,1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">First, mark the x-coordinate or the horizontal distance along the x-axis and later, mark the vertical distance using the y-coordinate.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"583\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-12.png\" alt=\"Plotting coordinates on cartesian plane\" class=\"wp-image-14447\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-12.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-12-300x282.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"8-facts\">Facts<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates hold significance in maps. Often, maps use a letter as one of the coordinates for locating a point, and use a numeral for the other point. Coordinates in a map are given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"398\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-13.png\" alt=\"World map grid\" class=\"wp-image-14448\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-13.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Coordinates-13-300x193.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The x-coordinate of a point is also known as \u201cabscissa.\u201d It is pronounced as \u2018\u2018ab-SISS-ah\u2019\u2019 (the \u201cc\u201d is silent). The term \u201cx-coordinate\u201d is most commonly used.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The y-coordinate is also called the \u201cordinate.\u201d You can pronounce it as \u201cORD-inet.\u201d The term \u201cy-coordinate\u201d is preferred.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about coordinates of a point, their representation, plotting a point on the cartesian plane along with two types of coordinates.&nbsp;<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"10-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Plot the given point on a graph: P(2, 5).<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since both the values of x and y are positive, the point lies in the 1st quadrant.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The point is 2 units to the right of origin along the x-axis and 5 units up.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The given point on a graph can be plotted as-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"442\" height=\"391\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-1.png\" alt=\"Coordinate points on a cartesian plane\" class=\"wp-image-14449\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-1.png 442w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-1-300x265.png 300w\" sizes=\"auto, (max-width: 442px) 100vw, 442px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Plot the given point on a graph: P<\/strong>$(-3,4)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the value of x is positive and y is negative, hence the point lies in the third quadrant. The given point on a graph can be plotted as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"449\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-4.png\" alt=\"Coordinate points on a cartesian plane\" class=\"wp-image-14451\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-4.png 450w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-4-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-4-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-4-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-4-120x120.png 120w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Plot the given point on a graph: P<\/strong>$(3, -2)$<strong> and identify the quadrant it lies in.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since both the values of x and y are negative, the point lies in the 3rd quadrant. The given point on a graph can be plotted as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"449\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2.png\" alt=\"Coordinate points on a cartesian plane\" class=\"wp-image-14450\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2.png 450w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-120x120.png 120w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find the corresponding cartesian coordinates if the polar coordinates of a point are <\/strong>$(2, 30\\circ)$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = r$ $cos \\theta$ and $y = r$ $sin \\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $x = 2$ $cos30^\\circ$ and $y = 2$ $sin30^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 2 (\\frac{\\sqrt{3}}{2})$ and $y = 2 (\\frac{1}{2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\sqrt{3}$ and $y = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Cartesian coordinates are $(\\sqrt{3},1)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Plot the given point on a graph: P(4, 4)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since both the values of x and y are positive, the point lies in the 1st quadrant. The given point on a graph can be plotted as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"449\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-5.png\" alt=\"Coordinate points on a cartesian plane\" class=\"wp-image-14452\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-5.png 450w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-5-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-5-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-5-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-5-120x120.png 120w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"11-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Coordinates<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Identify the quadrant in which the point P$(-5, -5)$ lies.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">I<\/div><div class=\"spq_answer_block\" data-value=\"1\">II<\/div><div class=\"spq_answer_block\" data-value=\"2\">III<\/div><div class=\"spq_answer_block\" data-value=\"3\">IV<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: III<br\/>Since both the values of x and y are negative, the point lies in the 3rd quadrant.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the \u201cordinate\u201d in (5, 8)?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">0<\/div><div class=\"spq_answer_block\" data-value=\"3\">13<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8<br\/>The y-coordinate is known as the ordinate. In the ordered pair $(5, 8), 5$ is the abscissa and 8 is the ordinate.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following points lies on the Y-axis? $(0, 4), (0, 2)$ and $(0, -3)$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(0, -3)$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(0, 4)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">All<\/div><div class=\"spq_answer_block\" data-value=\"3\">None<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: All<br\/>The x-coordinate of all the points is 0. So, all the points lie on the y-axis.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The points $(-1, 0), (2, 0)$ and $(5, 0)$ lie on$ \\underline{}$ .<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">the x-axis<\/div><div class=\"spq_answer_block\" data-value=\"1\">the y-axis<\/div><div class=\"spq_answer_block\" data-value=\"2\">both the axes<\/div><div class=\"spq_answer_block\" data-value=\"3\">the line x $=$ y<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: the x-axis<br\/>The y-coordinate of all the points is 0. So, all the points lie on the x-axis.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-2.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The points $(7, 8), (3, 6)$ and $(8, 2)$ lie on Quadrant$\\underline{}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">I<\/div><div class=\"spq_answer_block\" data-value=\"1\">II<\/div><div class=\"spq_answer_block\" data-value=\"2\">III<\/div><div class=\"spq_answer_block\" data-value=\"3\">IV<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: I<br\/>The points $(7, 8), (3, 6)$ and $(8, 2)$ have positive coordinates. So, the points lie in the first quadrant.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-3.png\"><\/div><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Coordinates\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Coordinates\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the quadrant in which the point P$$(-5, -5)$$ lies.\",\n                    \"text\": \"Identify the quadrant in which the point P$$(-5, -5)$$ lies.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Since both the values of x and y are negative, the point lies in the 3rd quadrant.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"I\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since both the values of x and y are negative, the point lies in the 3rd quadrant.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"II\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since both the values of x and y are negative, the point lies in the 3rd quadrant.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"IV\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since both the values of x and y are negative, the point lies in the 3rd quadrant.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"III\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Since both the values of x and y are negative, the point lies in the 3rd quadrant.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Since both the values of x and y are negative, the point lies in the 3rd quadrant.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the \u201cordinate\u201d in (5, 8)?\",\n                    \"text\": \"What is the \u201cordinate\u201d in (5, 8)?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The y-coordinate is known as the ordinate. In the ordered pair $$(5, 8), 5$$ is the abscissa and 8 is the ordinate.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The y-coordinate is known as the ordinate. In the ordered pair (5, 8), 5 is the abscissa and 8 is the ordinate.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The y-coordinate is known as the ordinate. In the ordered pair (5, 8), 5 is the abscissa and 8 is the ordinate.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The y-coordinate is known as the ordinate. In the ordered pair (5, 8), 5 is the abscissa and 8 is the ordinate.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The y-coordinate is known as the ordinate. In the ordered pair (5, 8), 5 is the abscissa and 8 is the ordinate.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The y-coordinate is known as the ordinate. In the ordered pair (5, 8), 5 is the abscissa and 8 is the ordinate.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following points lies on the Y-axis? $$(0, 4), (0, 2)$$ and $$(0, -3)$$.\",\n                    \"text\": \"Which of the following points lies on the Y-axis? $$(0, 4), (0, 2)$$ and $$(0, -3)$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The x-coordinate of all the points is 0. So, all the points lie on the y-axis.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(0, -3)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The x-coordinate of all the points is 0. So, all the points lie on the y-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(0, 4)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The x-coordinate of all the points is 0. So, all the points lie on the y-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The x-coordinate of all the points is 0. So, all the points lie on the y-axis.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"All\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The x-coordinate of all the points is 0. So, all the points lie on the y-axis. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-1.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The x-coordinate of all the points is 0. So, all the points lie on the y-axis. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-1.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The points $$(-1, 0), (2, 0)$$ and $$(5, 0)$$ lie on$$ \\\\underline{}$$ .\",\n                    \"text\": \"The points $$(-1, 0), (2, 0)$$ and $$(5, 0)$$ lie on$$ \\\\underline{}$$ .\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The y-coordinate of all the points is 0. So, all the points lie on the x-axis.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"the y-axis\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The y-coordinate of all the points is 0. So, all the points lie on the x-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"both the axes\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The y-coordinate of all the points is 0. So, all the points lie on the x-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"the line x $$=$$ y\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The y-coordinate of all the points is 0. So, all the points lie on the x-axis.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"the x-axis\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The y-coordinate of all the points is 0. So, all the points lie on the x-axis. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-2.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The y-coordinate of all the points is 0. So, all the points lie on the x-axis. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-2.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ lie on Quadrant$$\\\\underline{}$$.\",\n                    \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ lie on Quadrant$$\\\\underline{}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ have positive coordinates. So, the points lie in the first quadrant.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"II\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ have positive coordinates. So, the points lie in the first quadrant.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"III\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ have positive coordinates. So, the points lie in the first quadrant.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"IV\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ have positive coordinates. So, the points lie in the first quadrant.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"I\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ have positive coordinates. So, the points lie in the first quadrant. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-3.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The points $$(7, 8), (3, 6)$$ and $$(8, 2)$$ have positive coordinates. So, the points lie in the first quadrant. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-3.png\\\"\/>\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"12-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-6b244208-2dec-42c4-a969-686b1e49c660\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-6b244208-2dec-42c4-a969-686b1e49c660\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6b244208-2dec-42c4-a969-686b1e49c660\"><strong>What is the distance formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-6b244208-2dec-42c4-a969-686b1e49c660\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distance formula is used to calculate the distance between two points.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let the two points be A and B, having coordinates to be (x<sub>1<\/sub>, y<sub>1<\/sub>) and (x<sub>2<\/sub>, y<sub>2<\/sub>), respectively.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the distance between two points is given as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"57\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/faq.png\" alt=\"faq\" class=\"wp-image-17714\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/faq.png 347w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/faq-300x49.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-6b244208-2dec-42c4-a969-686b1e49c660\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6b244208-2dec-42c4-a969-686b1e49c660\"><strong>Who invented the Cartesian plane?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-6b244208-2dec-42c4-a969-686b1e49c660\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Ren\u00e9 Descartes first published the coordinate system in the seventeenth century.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-6b244208-2dec-42c4-a969-686b1e49c660\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6b244208-2dec-42c4-a969-686b1e49c660\"><strong>Which is latitude and longitude in coordinates?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-6b244208-2dec-42c4-a969-686b1e49c660\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates are represented as an ordered pair of two numbers. The first number is the latitude and the second is the longitude.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-6b244208-2dec-42c4-a969-686b1e49c660\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6b244208-2dec-42c4-a969-686b1e49c660\"><strong>What are three types of coordinate systems?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-6b244208-2dec-42c4-a969-686b1e49c660\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Three types of coordinates are: cartesian, polar and cylindrical.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-6b244208-2dec-42c4-a969-686b1e49c660\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6b244208-2dec-42c4-a969-686b1e49c660\"><strong>What are the uses of cartesian coordinates?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-6b244208-2dec-42c4-a969-686b1e49c660\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The x- and y-coordinates help us to locate any point in the coordinate axes, to find the distance between the two points and also to find the slope of a line.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Coordinates: Introduction Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space. You might have seen grids being used in math. What are these grids? These grids help us to plot any point using its coordinates. So, what are coordinates in math? Let us see the &#8230; <a title=\"Coordinates\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinates\" aria-label=\"More on Coordinates\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1519","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1519","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=1519"}],"version-history":[{"count":16,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1519\/revisions"}],"predecessor-version":[{"id":24695,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1519\/revisions\/24695"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1519"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1519"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}