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Answer :
To determine whether pool STUV is similar to pool WXYZ, we can follow these steps:
1. Translate WXYZ so that point W of WXYZ lies on point S of STUV:
- This step involves moving the entire pool WXYZ in such a way that point W coincides exactly with point S of the pool STUV. Translation is a process where all points of a shape are moved a certain distance in a certain direction.
2. Dilate WXYZ by the ratio [tex]\(\frac{\overline{TS}}{XW}\)[/tex]:
- After translating, we need to resize (dilate) pool WXYZ to test for similarity. Dilation involves scaling a shape larger or smaller while maintaining the proportion of its sides. Here, the dilation factor is given by the ratio of the length of [tex]\(\overline{TS}\)[/tex] (a side of pool STUV) to the length of [tex]\(\overline{XW}\)[/tex] (corresponding side of WXYZ).
- Mathematically, if [tex]\(\overline{TS}\)[/tex] is [tex]\(k\)[/tex] times the length of [tex]\(\overline{XW}\)[/tex], we need to multiply every side length of pool WXYZ by [tex]\(k\)[/tex].
After these transformations, if the corresponding angles between the sides of both pools remain the same and the side lengths of pool WXYZ (post dilation) match the side lengths of pool STUV proportionality, then pools STUV and WXYZ are indeed similar by definition of similarity in geometry.
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]\(\frac{\overline{TS}}{XW}\)[/tex]."
1. Translate WXYZ so that point W of WXYZ lies on point S of STUV:
- This step involves moving the entire pool WXYZ in such a way that point W coincides exactly with point S of the pool STUV. Translation is a process where all points of a shape are moved a certain distance in a certain direction.
2. Dilate WXYZ by the ratio [tex]\(\frac{\overline{TS}}{XW}\)[/tex]:
- After translating, we need to resize (dilate) pool WXYZ to test for similarity. Dilation involves scaling a shape larger or smaller while maintaining the proportion of its sides. Here, the dilation factor is given by the ratio of the length of [tex]\(\overline{TS}\)[/tex] (a side of pool STUV) to the length of [tex]\(\overline{XW}\)[/tex] (corresponding side of WXYZ).
- Mathematically, if [tex]\(\overline{TS}\)[/tex] is [tex]\(k\)[/tex] times the length of [tex]\(\overline{XW}\)[/tex], we need to multiply every side length of pool WXYZ by [tex]\(k\)[/tex].
After these transformations, if the corresponding angles between the sides of both pools remain the same and the side lengths of pool WXYZ (post dilation) match the side lengths of pool STUV proportionality, then pools STUV and WXYZ are indeed similar by definition of similarity in geometry.
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]\(\frac{\overline{TS}}{XW}\)[/tex]."
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