Question

Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 180° counterclockwise.

U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(4, 0), W′(1, 4)
U′(−1, 1), V′(4, 0), W′(1, −4)
U′(−1, 1), V′(0, −4), W′(−4, −1)

Answer 1

(a) U′(1, −1), V′(0, 4), W′(4, 1)

Explanation:

You want the coordinates of the image when ∆UVW is rotated 180° CCW.

Rotation 180°

Rotation 180° (either direction) is the same as reflection across the origin. It has the effect of reversing the sign of every coordinate:

(x, y) ⇒ (-x, -y) . . . . . rotation 180°

The image coordinates are ...

U(-1, 1) ⇒ U'(1, -1) . . . . . . matches choice A

V(0, -4) ⇒ V'(0, 4)

W(-4, -1) ⇒ W'(4, 1)

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