Rotation 90° counterclockwise about the origin
The coordinates of the pre-image are A (3 , -6) , B (1 , 2) , C (7 , -1)
Rotation 90° clockwise about the origin
The coordinates of the pre-image are A (-3 , 6) , B (-1 , -2) , C (-7 , 1)
Step-by-step explanation:
Let us revise the rotation
1. If point (x , y) rotated about the origin by angle 90° counter-clockwise
then its image is (-y , x)
2. If point (x , y) rotated about the origin by angle 90° clock wise
then Its image is (y , -x)
The given is:
After a rotation of 90° about the origin, the coordinates of the vertices
of the image of a triangle are A' (6 , 3), B' (-2 , 1) and C' (1 , 7)
We need to find the coordinates of the pre-image
There is no mention about the rotation counterclockwise or clockwise,
then we will do both
∵ The rotation is 90° counterclockwise about the origin
∵ Point A (x , y) and its image A' (-y , x)
∵ A' = (6 , 3)
∴ -y = 6 and x = 3
∵ -y = 6 ⇒ multiply both sides by -1
∴ y = -6
∴ Point A is (3 , -6)
∵ Point B (x , y) and its image B' (-y , x)
∵ B' = (-2 , 1)
∴ -y = -2 and x = 1
∵ -y = -2 ⇒ multiply both sides by -1
∴ y = 2
∴ Point B is (1 , 2)
∵ Point C (x , y) and its image C' (-y , x)
∵ C' = (1 , 7)
∴ -y = 1 and x = 7
∵ -y = 1 ⇒ multiply both sides by -1
∴ y = -1
∴ Point C is (7 , -1)
The coordinates of the pre-image are A (3 , -6) , B (1 , 2) , C (7 , -1)
∵ The rotation is 90° clockwise about the origin
∵ Point A (x , y) and its image A' (y , -x)
∵ A' = (6 , 3)
∴ y = 6 and -x = 3
∵ -x = 3 ⇒ multiply both sides by -1
∴ x = -3
∴ Point A is (-3 , 6)
∵ Point B (x , y) and its image B' (y , -x)
∵ B' = (-2 , 1)
∴ y = -2 and -x = 1
∵ -x = 1 ⇒ multiply both sides by -1
∴ x = -1
∴ Point B is (-1 , -2)
∵ Point C (x , y) and its image C' (y , -x)
∵ C' = (1 , 7)
∴ y = 1 and -x = 7
∵ -x = 7 ⇒ multiply both sides by -1
∴ x = -7
∴ Point C is (-7 , 1)
The coordinates of the pre-image are A (-3 , 6) , B (-1 , -2) , C (-7 , 1)
Learn more:
You can learn more about rotation in brainly.com/question/3779181
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