Question

1. select the sequence of rigid transformations and dilations that takes square (abcd) to square (efgh).

a. translate by the directed line segment (ae), which will take (b) to a point (b). then rotate with center (e) by angle (bef). finally, dilate with center (e) by scale factor (\frac{5}{2}).
b. translate by the directed line segment (ae), which will take (b) to a point (b). then rotate with center (e) by angle (bef). finally, dilate with center (e) by scale factor (\frac{2}{5}).
c. dilate using center (e) by scale factor (\frac{2}{5}).
d. dilate using center (e) by scale factor (\frac{5}{2}).

Explanation:

Step1: Identify scale factor

The side length of square ABCD is 5, and square EFGH is 2. The scale factor from ABCD to EFGH is $\frac{2}{5}$.

Step2: Check transformation sequence

To map ABCD to EFGH, we need to dilate ABCD by scale factor $\frac{2}{5}$ with center E (since E is the corresponding vertex of A, and dilation center should align the figures).

Answer:

c. Dilate using center E by scale factor $\frac{2}{5}$.