# Point – Definition With Examples

## What is a Point in Math?

When we try to show directions to a friend using pen and paper, we simply draw dots and name them to show the location of the benchmarks and the destination for our convenience. Similarly, a point in math (or, in geometry, to be specific) is a tiny dot used to show a location in space.

## Definition of Point in Mathematics

In math, a point is represented by a dot (.) and is used to tell exact location in space. It does not have any length, width, or height. In other words, it has no size. A point is usually named using uppercase letters.

Let’s have a look at some points — A, B, C, and D.

## Using Points to Find a Location

Given below is a treasure hunt map. Let’s locate the position of each hidden object.

In the above image, the location of the ring is point A, the hat is at point B, the bat is point C and a dinosaur is at point D.

## Point of Intersection

When two lines intersect each other, they cross each other at a point known as the point of intersection. In the given image, O is the point of intersection of lines a and b.

## Types of Points

There are different types of points in geometry:

• Collinear Points

Collinear means something in the same line. Three or more points are said to be collinear if they lie on a single straight line.

In the above figure, points A, B and C lie on the same line. So, they are collinear points.

• Non-collinear Points

Three or more points are said to be non-collinear if they do not lie on the same line. We can not draw a single straight line that passes through all these points.

In the above figure, there is no single straight line that can pass through all these points in one go, so the points are non-collinear.

• Coplanar Points and Non-coplanar Points

Two or more points are said to be coplanar if they lie on the same plane. Two or more points are said to be non-coplanar if they do not lie on the same plane.

In the above figure, points A, B, and C are coplanar whereas point D is non-coplanar as it does not lie on the same plane M. In the above figure, the points A, B, and C lie on the same plane M, and hence, they are coplanar. Since the point D does not lie on the plane M, it is non-coplanar with the points A, B, and C.

• Concurrent Points

Concurrent point is the point where three or more lines intersect each other.

Lines l, m and n intersect each other at point O. That means A is the concurrent point or the point of concurrency.

## Point in the Cartesian Plane

A point on a Cartesian plane has a unique location known as coordinates. It holds the information on how far along and how far up the point is from the origin. The coordinates of a point are expressed as an ordered pair P (x, y), where x is the horizontal distance and y is the vertical distance.

In the above figure, P is the point that is represented by (x,y).

The x-value tells how the point moves either to the right or left along the x-axis

If x-coordinate is positive, then it will be on the right side of the origin. And if the

x-coordinate is negative, then it will be on the left side of the origin.

Similarly, the y-value tells how the point moves either up or down along the y-axis

If y-coordinate is positive, then it will be upwards from the origin. And if the y-coordinate is negative, then it will be below the origin.

For example: A point (3, 5) is represented in the graph given below.

## Solved Examples

1. What will be the ordered pair for the point for the given value of x and y coordinates if x = – 6 units and y = 4 units?

Solution: The ordered pair is written in the form (x, y) where x denotes the distance along the x-axis and y denotes the distance on the y-axis (vertical axis). So, corresponding to the given values of x and y, the point will be: (–6, 4).

2. Plot the point (6,-4) on the graph.

Solution:

3. What is the point P called?

Solution: P is called the point of concurrency

## Practice Problems

1

### Three or more points that lie on the same line are known as _______ points.

concurrent
coplanar
collinear
non-collinear
CorrectIncorrect
Collinear points are the points that lie on the same line.
2

### If the ordered pair for the point for the given value of x and y coordinates is $(4$, $–$ $7)$, then what will be the value of y?

$7$
$4$
$-$ $7$
$-$ $4$
CorrectIncorrect
Correct answer is: $-$ $7$
The ordered pair is of the form $(\text{x}, \text{y})$. So, $\text{y} =$ $–$ $7$
3

### Which of the following does a point have?

length
width
thickness
None of these
CorrectIncorrect
Correct answer is: None of these
A point does not have any length, width or thickness.