Question

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 \\( \frac { 4 } { 3 } \\). yes, because both figures are rectangs and all rectangles are similar. no, because the center of dilation is not at \\( ( 0,0 ) \\). no, because corresponding s es have different slopes.

Explanation:

Step1: Check similarity condition

For a dilation, corresponding sides of the pre - image and image should be parallel and the ratio of their lengths should be constant.

Step2: Analyze other options

• Option B: Not all rectangles are similar. Similarity requires side - length ratios to be equal.
• Option C: The center of dilation is at the origin as per the problem statement.
• Option D: Corresponding sides of rectangles EFGH and ABCD are parallel (since they are rectangles, opposite sides are parallel and for dilation, corresponding sides remain parallel).

Answer:

A. Yes, because corresponding sides are parallel and have lengths in the ratio \(\frac{4}{3}\).