Question

A pool company is creating a blueprint for a family pool and a similar dog pool for a new client. Which statement explains how the company can determine whether pool ABCD is similar to pool EFGH?

quadrilaterals ABCD and EFGH

Translate EFGH so that point F of EFGH lies on point B of ABCD, then dilate EFGH by the ratio segment EF over segment AB.
Translate EFGH so that point E of EFGH lies on point A of ABCD, then translate EFGH so that point F of EFGH lies on point B of ABCD.
Translate EFGH so that point E of EFGH lies on point A of ABCD, then dilate EFGH by the ratio segment AB over segment EF.
Translate EFGH so that point F of EFGH lies on point B of ABCD, then translate EFGH so that point E of EFGH lies on point A of ABCD.

Answer 1

The correct statement is:

Translate EFGH so that point F of EFGH lies on point B of ABCD, then dilate EFGH by the ratio segment EF over segment AB.

Effect of the transformation

This sequence of transformations ensures that corresponding vertices of the quadrilaterals ABCD and EFGH are brought into coincidence through translation, and then a dilation is applied with the specified ratio.

This series of transformations preserves the shape and orientation of the quadrilaterals, indicating similarity.

Translating EFGH so that point F lies on point B ensures that corresponding vertices are aligned. This forms shape E'F"G'H' in the figure

Dilating E'F'G'H' by the ratio segment EF over segment AB ensures that the corresponding sides are proportional.

In the image, the ratio segment is 2. So, the dilation factor is 2.

EFGH * 2 = ABCD