Reflection of Geometrical Figures
Subject: Compulsory Maths
Overview
The reflection of a geometrical figure means the formation of the image of the figure after reflecting the figure about the line of reflection.Reflection of Geometrical Figures
Reflection in Geometrical Figures
The reflection of a geometrical figure means the formation of the image of the figure after reflecting the figure about the line of reflection.
Properties of Reflection
- There should be equal distance between the geometrical figure and its image from the line of reflection.
- The areas of the geometrical figure and its image are equal.
- The appearance of the image of a figure is opposite to figure.
Reflection of geometrical figures using coordinates
Here, we can find the co-ordinates of the images of geometrical figures formed due to the reflection by x-axis and y-axis separately. In this case, x-axis and y-axis are called the axis of reflection.
- X-axis as the axis of reflection
When a geometrical figure is reflected about x-axis as the axis of reflection, the x-coordinate of the image remains the same and the sign of y-coordinate of the image as changed.
- Y-axis as the axis of reflection
When a geometrical figure is reflected about y-axis as the axis of reflection, the sign of x-coordinate of the image is changed but the y-coordinate of the image remains the same.
Things to remember
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Properties of Reflection
- There should be equal distance between the geometrical figure and its image from the line of reflection.
- The areas of the geometrical figure and its image are equal.
- The appearance of the image of a figure is opposite to figure.
- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.
Videos for Reflection of Geometrical Figures
Translations Reflections and Rotations
Math Shorts Episode 4 - Reflection
Questions and Answers
Draw a graph when A(2,-2), B(5,3) and C(1,4) are the vertices of \(\triangle\)ABC. When \(\triangle\)ABC is reflected about y-axis.
Solution:
A(2,-2)\(\rightarrow\)A’(-2,-2)
B(5,3)\(\rightarrow\)B’(-5,3)
C(1,4)\(\rightarrow\)C’(-1,4)
So, the coordinates of the vertices of image \(\triangle\)A’B’C’ are A(-2,-2), B(-5,3) and C(-1,4).
Draw a graph when A(-2,3), B(2,1) and C(4,4) are the vertices of \(\triangle\)ABC. When \(\triangle\)ABC is reflected about x-axis.
Solution:
A(-2,3)\(\rightarrow\)A’(-2,-2)
B(2,1)\(\rightarrow\)B’(2,-1)
C(4,4)\(\rightarrow\)C’(4,-4)
So, the coordinates of the vertices of image \(\triangle\)A’B’C’ are A(-2,-3), B(2,-1) and C(4,-4).
Define axis of reflection.
When the coordinates of the images of geometrical figures formed due to the reflection by x - axis and y - axis, then in this case x-axis and y-axis are called the axis of reflection.
Find the images of the following points separately under the reflection about x-axis and y-axis.
- (2, 6)
- (4, -7)
Solution:
| Points | x-axis | y-axis |
| A(2, 6) | A'(2, -6) | A"(-2, 6) |
| B(4, -7) | B'(4, 7) | B"(-4, -7) |
Copy the following figures in your graph paper and draw their images under the reflection about x-axis. Also, mention the coordinates of the vertices of images.
a)
Figure a) \(\triangle\)ABC = A'(3 -4), B'(1, -2), C'(4, -1)
Figure b) \(\triangle\)DEF = D'(-3, -1), E'(0, -5), F'(-5, -3)
Quiz
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