Sample Example on Point Symmetry
Example 1: State whether the following statement is true or false: “Every equilateral triangle exhibits point symmetry.”
Solution:
True. Every equilateral triangle exhibits point symmetry. In an equilateral triangle, the point of symmetry is the center of the triangle, where all three medians intersect. This means that if you fold the equilateral triangle along its center, the two resulting halves will perfectly overlap, demonstrating point symmetry.
Example 2: A figure has a point symmetry at the origin. If point B(-2, 5) is part of the figure, find the coordinates of its image point.
Solution:
Point symmetry involves reflecting a point across a central point (in this case, the origin). When a point is symmetrically located with respect to the origin, its coordinates become the negation of the original coordinates.
For point B(-2, 5), the image point (let’s call it B’) can be found by negating the coordinates:
B’ = (-(-2), -(5))
= (2, -5)
Therefore, the image point B’ is (2, -5).
Point Symmetry
Point Symmetry, or Origin Symmetry, or Central Symmetry is a type of symmetry where an object or shape looks the same when rotated 180° (a half-turn) around a central point.
In this article, we will discuss Point Symmetry in detail including its definition, examples, as well as some real-life examples in nature as well.
Table of Content
- What is Symmetry?
- What is Point Symmetry?
- How to Identify Point Symmetry?
- Point Symmetry in Geometric Shapes
- Point Symmetry of Square/Rectangle
- Point Symmetry of Parallelogram
- Point Symmetry of a Circle
- Point Symmetry of a Star
- Point Symmetry in Letters
- Point Vs Reflection Symmetry
- Sample Example
- Point Symmetry: FAQs