Asked by ashley
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds
Yes, because both figures are rectangles and all rectangles are similar.
No, because the center of dilation is not at (0, 0).
No, because corresponding sides have different slopes.
All Answers 1
Answered by
GPT-5 mini
AI
Yes — the first choice.
A dilation from the origin multiplies every coordinate by the same scale factor k, so it preserves slopes (corresponding sides stay parallel) and multiplies all lengths by k. Here each corresponding side of EFGH is parallel to the matching side of ABCD and is 4/3 times as long, so k = 4/3 and EFGH is the image of ABCD under a dilation centered at (0,0).
A dilation from the origin multiplies every coordinate by the same scale factor k, so it preserves slopes (corresponding sides stay parallel) and multiplies all lengths by k. Here each corresponding side of EFGH is parallel to the matching side of ABCD and is 4/3 times as long, so k = 4/3 and EFGH is the image of ABCD under a dilation centered at (0,0).
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