POINT SYMMETRY

A figure has point symmetry, if it has a rotational symmetry of 180 degrees.

How to check if a shape has symmetry about a point : 

One way to check if a figure has symmetry about a point would be to turn it upside down. If the figure looks the same as the original then it has symmetry about a point.

However, we can use the following two conditions to check whether a shape has  symmetry about a point. 

(i) Every part of the given shape must have a matching part must be at the same distance from the central  point

(ii) The part of the shape and its matching part must be in the opposite direction. 

Note :

Symmetry about a point is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is symmetrical.

Example :

Practice Problems

Problem 1 :

State if playing card given below has symmetry about a point. 

Solution : 

Yes

In the playing card given above, we have

(i) Every part of the card has a matching part are at the same distance from the central  point.

(ii) The part of the playing card and its matching part are in the opposite direction. 

More clearly, 

Problem 2 :

State if the shape given below has symmetry about a point. 

Solution : 

Yes

In the shape given above, we have

(i) Every part of the shape has a matching part are at the same distance from the central  point.

(ii) The part of the shape and its matching part are in the opposite direction. 

More clearly, 

Problem 3 :

State if the shape given below has symmetry about a point. 

Solution : 

No 

The shape given above does not satisfy the second condition of point of symmetry. 

That is, 

The part of the shape and its matching part are not in the opposite direction. They are in the same direction.

More clearly, 

Problem 4 :

State if the shape given below has symmetry about a point. 

Solution : 

Yes

In the shape given above, we have

(i) Every part of the shape has a matching part are at the same distance from the central  point.

(ii) The part of the shape and its matching part are in the opposite direction. 

More clearly, 

Problem 5 :

State if the shape given below has symmetry about a point. 

Solution : 

No 

The shape given above does not satisfy the first condition of point of symmetry. 

That is, 

The part of the shape and its matching part are not at the same distance from the central  point.

More clearly, 

Problem 6 :

State if the shape given below has symmetry about a point. 

Solution : 

Yes

In the shape given above, we have

(i) Every part of the shape has a matching part are at the same distance from the central  point.

(ii) The part of the shape and its matching part are in the opposite direction. 

More clearly, 

Problem 7 :

State if the shape given below has symmetry about a point. 

Solution : 

Yes

In the shape given above, we have

(i) Every part of the shape has a matching part are at the same distance from the central  point.

(ii) The part of the shape and its matching part are in the opposite direction. 

More clearly, 

Problem 8 :

State some English alphabets which exhibit symmetry about a point. 

Solution : 

The English alphabets Z, H, N and O exhibit point symmetry. 

More clearly, 

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