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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). What are the coordinates of the vertices of the pre-image?

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Answer:

A(-3, 6), B(-1, -2), C(-7, 1)

Step-by-step explanation:

To the pre-image after a 270°-counterclockwise rotation [90°-clockwise rotation], just reverse it by doing a 270°-clockwise rotation [90°-counterclockwise rotation]:

Extended Rotation Rules

  • 270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)
  • 270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)
  • 180°-rotation >> (x, y) → (-x, -y)

So, perform your rotation:

270°-clockwise rotation [90°-counterclockwise rotation] → C'[1, 7] was originally at C[-7, 1]

→ B'[-2, 1] was originally at B[-1, -2]

→ A'[6, 3] was originally at A[-3, 6]

I am joyous to assist you anytime.

Answer:

A: (3, -6)

B: (1, 2)

C: (7, -1)

Step-by-step explanation:Just got it right!

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