Question
segment A prime B prime has endpoints located at A′ (0, 0) and B′ (2, 0). It was dilated at a scale factor of one half from center (2, 0). Which statement describes the pre-image?
segment AB is located at A (−2, 0) and B (2, 0) and is half the length of segment A prime B prime.
segment AB is located at A (−2, 0) and B (2, 0) and is twice the length of segment A prime B prime.
segment AB is located at A (−1, 0) and B (1, 0) and is half the length of segment A prime B prime.
segment AB is located at A (−1, 0) and B (1, 0) and is twice the length of segment A prime B prime.
segment AB is located at A (−2, 0) and B (2, 0) and is half the length of segment A prime B prime.
segment AB is located at A (−2, 0) and B (2, 0) and is twice the length of segment A prime B prime.
segment AB is located at A (−1, 0) and B (1, 0) and is half the length of segment A prime B prime.
segment AB is located at A (−1, 0) and B (1, 0) and is twice the length of segment A prime B prime.
Answers
Answered by
GPT-5 mini
"segment AB is located at A (−2, 0) and B (2, 0) and is twice the length of segment A′B′."
Reason: For dilation with center C = (2,0) and scale k = 1/2, A = C + (1/k)(A′ − C) = (2,0) + 2[(0,0) − (2,0)] = (−2,0); B = (2,0) + 2[(2,0) − (2,0)] = (2,0). AB has length 4, A′B′ length 2, so AB is twice A′B′.
Reason: For dilation with center C = (2,0) and scale k = 1/2, A = C + (1/k)(A′ − C) = (2,0) + 2[(0,0) − (2,0)] = (−2,0); B = (2,0) + 2[(2,0) − (2,0)] = (2,0). AB has length 4, A′B′ length 2, so AB is twice A′B′.
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