Question

ms. romano draws figures a and a on the board. a. are figures a and a similar? explain. b. marcus says figure a is dilated to form figure a using a scale factor of 2 and point b as the center of dilation. what mistake did marcus make? what is the correct relationship?

Explanation:

Step1: Analyze dilation concept

Dilation changes size proportionally. If scale - factor is 2, all distances from center of dilation to corresponding points on the figure should double.

Step2: Check Marcus's claim

By observing the grid and the figures, if we measure distances from point B to corresponding points on A and A', we can see that the distances do not double. Figure A' is smaller than what would be formed by a scale - factor of 2 dilation from B.

Step3: Determine correct relationship

The correct relationship is that figure A' is formed from figure A by a scale factor less than 1 (it is a reduction, not an enlargement as Marcus thought).

Answer:

Marcus's mistake is that he thought the scale factor was 2 (an enlargement), but in fact figure A' is a reduction of figure A with a scale factor less than 1.