In this chapter we will learn about point symmetry with property and solved examples.

## What is Point Symmetry ?

An image is said to be in point symmetry when;

(a) there is center point O

(b) there is a matching part of image equidistant from center point O

(c) the matching part is in opposite direction.

**Note:**

Across the center point O, the point symmetry image looks the same upside down.

### How is line symmetry different from point symmetry ?

**In line symmetry**, the line is the reference to divide the image into two equal parts such that the parts are mirror image of each other.

Features of Line symmetry are;

(a) Line divides the given shape

(b) shape is divided into two parts

(c) the parts are mirror image of each other

**In point symmetry**, the central point is the reference to check the given shape.

Around the center point O, we will get the same part of image in the opposite direction.

## Examples of Point Symmetry

Consider the above image with two stars.

Locating the center point o for the above image.

Here O is the center point of the given image.

Note that at same distance from central point O with get the matching part of the image.

Hence, both the two stars are exact replica of each other but placed in opposite direction.

**Example 02**

Check if the below image is point symmetry or not.

**Solution**

First locate the center point O in the given image.

Here O is the center point.

Noe check if we get the same part equidistant from center point.

Equidistant from center point O & in opposite direction we get the same type of parts.

Hence, the given image is point symmetry.

**Example 03**

Check if below shape is in point symmetry?

**Solution**

For checking the point symmetry, first find the center point O.

Note that equidistant from point O, we will get similar parts of the image.

Since the image looks the same upside down, it is a point symmetry.

**Example 04**

Given below is point symmetry example of square, rectangle and parallelogram.

If we cut the above quadrilateral across the red line, we will get the same view on both sides.

**Example 05**

Check the point symmetry of below image.

**Solution**

Find the center point of above image and check if we can get matching parts at same distance from central point.

From center point O, the image look the same upside down.

Hence the image is in point symmetry.