Question

15) If the point (6, 3) is rotated 180° clockwise about

(2,9), what are the coordinates of the new point?
A. (15,-2)
B. (-2, 15)
C. (1, 12)
D. (12, 1)

Answer 1

B. (-2, 15)

Explanation:

Pretend that your fixed point [2, 9] is at the origin for now by translating it two units west then nine units south [0, 0]. Now, the same goes for [6, 3]. Translate it two units west then nine units south to get [4, -6]. Then, according to the 180°-rotation rule, you take the OPPOSITE of both the x-coordinate and y-coordinate:

[4, -6] → [-4, 6]

Now, that you have your rotated point, we have to shift EVERYTHING BACK to the way it was from when we shifted the fixed point of [2, 9] to the origin. We do that by translating everything in reverse order, which is 9 blocks north then 2 blocks east:

→ [0, 0] back to [2, 9]

Translation

→ [-4, 6] to the new coordinate of [-2, 15]

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