Question

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)

Answer 1

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:

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