To determine whether pool STUV is similar to pool WXYZ, you have to check if there is a sequence of transformations that maps one pool to the other and maintains the proportions of their sides and angles.
Among the given statements:
a) Translate WXYZ so that point \(W\) of WXYZ lies on point \(S\) of STUV, then translate WXYZ so that point \(X\) of WXYZ lies on point \(T\) of STUV.
This sequence of transformations involves two translations, but it might not necessarily preserve the similarity since it doesn’t consider scaling to maintain proportion.
b) Translate WXYZ so that point \(X\) of WXYZ lies on point \(T\) of STUV, then dilate WXYZ by the ratio \(\frac{\overline{XW}}{\overline{TS}}\).
This method is correct because:
- Translating WXYZ so that point \(X\) lies on point \(T\) aligns one side of the pool.
- Dilating WXYZ by the ratio \(\frac{\overline{XW}}{\overline{TS}}\) scales WXYZ proportionally to match STUV if they truly are similar shapes.
This sequence ensures that all corresponding sides are proportional and angles are preserved, confirming the similarity.
c) Translate WXYZ so that point \(X\) of WXYZ lies on point \(S\) of STUV, then translate WXYZ so that point \(W\) of WXYZ lies on point \(T\) of STUV.
This sequence is similar to option a) with only translations and does not ensure the proportions are preserved.
Thus, the correct statement that explains how the company can determine whether pool STUV is similar to pool WXYZ is:
b) Translate WXYZ so that point \(X\) of WXYZ lies on point \(T\) of STUV, then dilate WXYZ by the ratio \(\frac{\overline{XW}}{\overline{TS}}\).
This option correctly aligns and scales the pools to check for similarity.
