is rectangle efgh the result of a dilation of rectangle abcd with a center of dilation at the origin? why or…

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 rectangles and all rectangles are similar. no, because the center of dilation is not at (0, 0). no, because corresponding sides have different slopes.

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 rectangles and all rectangles are similar. no, because the center of dilation is not at (0, 0). no, because corresponding sides have different slopes.

Answer

Answer:

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

Explanation:

Step1: Recall dilation properties

In dilation from origin, corresponding - sides of pre - image and image are parallel and the ratio of their lengths is the scale factor.

Step2: Analyze option A

If corresponding sides are parallel and have a constant ratio of lengths, it is a dilation. This option satisfies the properties of dilation from the origin.

Step3: Analyze option B

Just because two figures are rectangles does not mean one is a dilation of the other. Similarity is not enough to confirm dilation from a specific center (the origin here).

Step4: Analyze option C

The center of dilation is stated to be at the origin in the problem, so this option is incorrect.

Step5: Analyze option D

In a dilation from the origin, corresponding sides should be parallel (have the same slopes), not different slopes. So this option is incorrect.