Asked by julie
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
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A dilation with scale factor 1/4 and then a translation.
Reason: each side length of A'B'C'D' is 1/4 of the corresponding side of ABCD (e.g. AB = 8, A'B' = 2; BC = 4, B'C' = 1), and the directions of corresponding sides match, so no rotation is needed. Thus a 1/4 dilation followed by a translation maps ABCD to A'B'C'D'.
Reason: each side length of A'B'C'D' is 1/4 of the corresponding side of ABCD (e.g. AB = 8, A'B' = 2; BC = 4, B'C' = 1), and the directions of corresponding sides match, so no rotation is needed. Thus a 1/4 dilation followed by a translation maps ABCD to A'B'C'D'.
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