Point Symmetry: In geometry, there are different aspects associated with symmetry, and students need to understand the concept of symmetry. This concept is used by artists, professionals, clothes and jewellery designers, automobile manufacturers, architects, and others for different tasks associated with their respective professions. There are symmetrical motifs everywhere: beehives, flowers, tree leaves, religious symbols, rugs, and handkerchiefs.

You can demonstrate point symmetry by walking up to a mirror and touching the mirror with your finger. The point is where your finger touches the mirror. It is as though you are inextricably bound to your image. An essential principle in point symmetry is that there must be a connection. When you turn an object upside-down and look the same, it is said to have point symmetry. The shape and the matching elements must face the same way.

Point Symmetry: Definition

When every part has a matching part, this is known as point symmetry. It is the same distance but in the opposite direction from the centre point. It’s also known as “Order \(2\) rotational symmetry.”

However, the following two requirements can be used to determine whether a form has symmetry around a point.

1. Every part of the specified shape must be at the same distance from the central point as the other parts.
2. The shape’s part and its corresponding part must be in the opposite direction.

Note: Because the “Origin” is the primary point around which the shape is symmetrical, point symmetry is also known as origin symmetry.

Point Symmetry: Examples

When there is a position or a central point on an object, point symmetry arises. The central point separates the object or shape into two portions. Each portion has a corresponding part on the other that is the same distance from the central point. Both pieces are positioned in opposite directions.

When a figure is drawn around a single point, it has point symmetry. This location is known as the figure’s centre or the symmetry’s centre. In the adjacent figure, we can see a point \(X’\) on the other side of the centre that corresponds to point \(X\) on the figure and is immediately opposite to \(X\) and lies on the figure. The figure is said to be symmetrical around the centre.

When we rotate a figure \({180^ \circ }\), and it regains its original shape, we claim it has point symmetry.

Point Symmetry in Letters

The symmetry point is a location that acts as a sort of “centre” for the figure. If you draw a line through the point of symmetry and it crosses the figure on one side of the point, the line will cross the figure on the other side of the point at the same distance from the point.

If every portion of an object has a matching part, it is said to have point symmetry. Point symmetry can be found in many letters of the English alphabet. The central point is \(O\) and the corresponding sections are in opposing directions.

Point symmetry exists in the capital letters \(H,\,\,I,\,N,\,\,O,\,X\) and \(O\)  Point and line symmetry can be found in the letters \(H,\,\,I,\,O,\) and \(X\)

Point Symmetry: Shapes

An object or shape has point symmetry if two similar shapes are formed by inserting a point on the object or shape, but they face different directions. It’s like you are splitting the object in half so that both sides are the same but facing a different direction.

Some geometrical shapes like squares and rectangles have a point of symmetry. When we rotate the shapes square and rectangle about \({180^ \circ }\) we regain the original shape.

The symmetry centre is \(O\) in this case. There is an \(X’\)  regarding \(X\) which is directly opposite \(X\)  on the other side of \(O\)

Solved Examples – Point Symmetry

Q.1. Which of the following letters has a point symmetry but does not have a line of symmetry?
a) \(H\)
b) \(I\)
c) \(Z\)
d) \(X\)
Ans: If every portion of an object has a matching part, it is said to have point symmetry. Point symmetry can be found in many letters of the English alphabet. The central point is \(O\), and the corresponding sections are in opposing directions.
Point symmetry exists in the capital letters \(H,\,I,\,N,\,O,\,X,\,\) and \(Z\)
Line symmetry is an imaginary line that divides a figure into two identical parts.
Both point and line symmetry can be found in the letters \(H,\,\,I,\,\,O,\,\) and \(X\) But, for the letter \(Z\) although point symmetry is available, no line of symmetry is available.

Therefore, the correct answer is option a) \(Z\)

Q.2. Determine whether the shape below has symmetry around a point.

Ans: Yes, the given shape has symmetry around a point.
In shape mentioned above:
1. Every section of the shape has a corresponding part that is at the same distance from the centre.
2. The shape’s part and its corresponding part are in the opposite direction.
Clearly,

Q.3. Determine whether the shape below has symmetry around a point.

Ans: No, the given shape does not have symmetry around a point.
The shape mentioned above fails to meet the second symmetry point criteria.
That is, the shape’s part and its corresponding part are not in the opposite direction. They’re both heading in the same way.
Clearly,

Q.4. Give examples of English alphabets that have symmetry around a point.
Ans: The symmetry point is a location that acts as a sort of “centre” for the figure. If you draw a line through the point of symmetry and it crosses the figure on one side of the point, the line will cross the figure on the other side of the point at the same distance from the point.
The letters \(Z,\,\,H,\,\,N,\,\) and \(O\) of the English alphabet have point symmetry.

Q.5. Determine whether the shape below has symmetry around a point.

Ans: No, the given shape does not have symmetry around a point.
The above shape fails to meet the first criteria of point of symmetry.
The distance between the centre point and the part of the shape that matches it is not the same.
Clearly,

Summary

In this article, we learnt about the definition of point symmetry, examples of point symmetry, point symmetry letters, point symmetry shapes, solved examples on point symmetry, and FAQs on point symmetry.

The learning outcome of this article is the concept of symmetry is used by artists, professionals, clothes and jewellery designers, automobile manufacturers, architects, and many others.

Frequently Asked Questions (FAQs) based on Point Symmetry

Frequently asked questions related to point symmetry are listed as follows:

Q.3. What is the point symmetry of the letters?
Ans: If every portion of an object has a matching part, it is said to have point symmetry. Point symmetry can be found in many letters of the English alphabet. The central point is \(O\), and the corresponding sections are in opposing directions.

Q.4. Is point symmetry a type of symmetry?
Ans: An object or shape has point symmetry if, by inserting a point on the object or shape, two similar shapes are formed, but they face different directions. It’s like you are splitting the object in half so that both sides are the same but facing a different direction.

Q.5. Name a figure that has point symmetry?
Ans: When working with a circle, every line that passes through the centre is a symmetry line. There is an unlimited number of symmetrical lines. A figure exhibits point symmetry if it appears the same upside-down (rotated \({180^ \circ }\))  as it does right-side-up. Like the circle, many other geometrical shapes have a point of symmetry. Therefore, a circle is a figure that has point symmetry.

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