Question

is rectangle efgh the result of a dilation of rectangle abcd with a center of dilation at the origin? why or why not?
o yes, because corresponding sides are parallel and have lengths in the ratio 4/3.
o yes, because both figures are rectangles and all rectangles are similar.
o no, because the center of dilation is not at (0, 0).
o no, because corresponding sides have different slopes.

Explanation:

Step1: Recall dilation properties

For a dilation at origin, corresponding sides of pre - image and image are parallel and in proportion.

Step2: Analyze rectangles

Rectangles EFGH and ABCD have corresponding sides parallel. But if it were a dilation at origin, sides should be in proportion. Here, assume side lengths and check ratio. If not in same ratio, not a dilation at origin.

Answer:

No, because corresponding sides have different slopes.