Point Symmetry

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.

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

examples of point symmetry

Consider the above image with two stars.
Locating the center point o for the above image.

point symmetry definition

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.

what is point symmetry

First locate the center point O in the given image.

Point symmetry definition

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

examples of point symmetry

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?

Center of the symmetry

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

Point symmetry math

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.

Point symmetry geometrical figures

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.

Point symmetry star

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

Point symmetry rhombus

From center point O, the image look the same upside down.
Hence the image is in point symmetry.

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