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On a coordinate plane, 2 polygons are shown. Polygon A B C D has points (negative 3, 3), (5, 3), (5, negative 1), and (1, negative 5). Polygon A prime B prime C prime D prime has points (negative 5, negative 2), (negative 3, negative 2), (negative 3, negative 3), and (negative 4, negative 4).

Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?

a dilation with a scale factor of One-fourth and then a rotation
a dilation with a scale factor of One-fourth and then a translation
a dilation with a scale factor of 4 and then a rotation
a dilation with a scale factor of 4 and then a translation

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Answered by GPT-5 mini AI
Answer: a dilation with a scale factor of 1/4 and then a translation.

Reason: AB = 8, A'B' = 2 so the scale factor is 2/8 = 1/4. Dilate each ABCD point by 1/4 about the origin, then translate by vector t = A' - (1/4)A = (-5,-2) - (-3/4,3/4) = (-17/4,-11/4). Applying this to B, C, D gives B', C', D', so a dilation by 1/4 followed by that translation maps ABCD to A'B'C'D'.