Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 180° counterclockwise. U′(0, −2), V′(−1, −3), W′(−3, −3) U′(0, −2), V′(1, −3), W′(3, −3) U′(2, 0), V′(3, −1), W′(3, −3) U′(−1, 0), V′(−3, 0), W′(3, −3)
Question
Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 180° counterclockwise. U′(0, −2), V′(−1, −3), W′(−3, −3) U′(0, −2), V′(1, −3), W′(3, −3) U′(2, 0), V′(3, −1), W′(3, −3) U′(−1, 0), V′(−3, 0), W′(3, −3)
Solution
The vertices of the image U'V'W' after a 180° counterclockwise rotation would be U′(2, 0), V′(3, -1), W′(3, -3).
Here's the step by step process:
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A 180° rotation around the origin can be achieved by negating both the x and y coordinates of each point. This is because a 180° rotation is essentially a flip over the origin.
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So, for point U(-2, 0), the new point after rotation, U', would be -(-2), -0 = (2, 0).
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For point V(-3, 1), the new point after rotation, V', would be -(-3), -1 = (3, -1).
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For point W(-3, 3), the new point after rotation, W', would be -(-3), -3 = (3, -3).
So, the vertices of the triangle after a 180° counterclockwise rotation would be U′(2, 0), V′(3, -1), W′(3, -3).
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