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Answer :
To determine whether pool STUV is similar to pool WXYZ, we need to use a combination of geometric transformations: translation and dilation. Here’s a step-by-step explanation:
1. Translation:
- First, we need to align the two pools by translating pool WXYZ so that one of its points matches the corresponding point on pool STUV. We'll translate pool WXYZ so that point W of WXYZ lies on point S of STUV.
2. Dilation:
- After aligning point W with point S, we need to scale pool WXYZ to ensure that it is similar to pool STUV. To do this, we will dilate (resize) pool WXYZ by a specific ratio.
- The dilation ratio is determined by the comparison of corresponding sides of the two pools. Specifically, we will use the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex], where [tex]\(\overline{TS}\)[/tex] is the length of a side in pool STUV, and [tex]\(\overline{XW}\)[/tex] is the corresponding side length in pool WXYZ.
This combination of translation and dilation will preserve the shape and ensure that pool STUV and pool WXYZ are similar (having the same shape but possibly different sizes).
Thus, the correct statement is: "Translate WXYZ so that point W of WXYZ lies on point S of STUV, then dilate WXYZ by the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex]."
1. Translation:
- First, we need to align the two pools by translating pool WXYZ so that one of its points matches the corresponding point on pool STUV. We'll translate pool WXYZ so that point W of WXYZ lies on point S of STUV.
2. Dilation:
- After aligning point W with point S, we need to scale pool WXYZ to ensure that it is similar to pool STUV. To do this, we will dilate (resize) pool WXYZ by a specific ratio.
- The dilation ratio is determined by the comparison of corresponding sides of the two pools. Specifically, we will use the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex], where [tex]\(\overline{TS}\)[/tex] is the length of a side in pool STUV, and [tex]\(\overline{XW}\)[/tex] is the corresponding side length in pool WXYZ.
This combination of translation and dilation will preserve the shape and ensure that pool STUV and pool WXYZ are similar (having the same shape but possibly different sizes).
Thus, the correct statement is: "Translate WXYZ so that point W of WXYZ lies on point S of STUV, then dilate WXYZ by the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex]."
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