Subject: Compulsory Maths
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
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.
Properties of Reflection
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.
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)
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