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Answer :
To determine whether pool STUV is similar to pool WXYZ, we need to use transformations. When two shapes are similar, one can be obtained from the other using a combination of translations, rotations, reflections, and dilations.
Let's analyze the statements:
- Translation: This moves a shape without altering its size or orientation. It simply slides the shape to a new location without changing its dimensions.
- Dilation: This transformation changes the size of a shape but keeps its proportions constant. If one pool is a scaled version of the other, dilation will be involved in the transformation process.
Considering the options provided, we need to identify the statement that uses the correct transformations to determine similarity:
1. Choice (a): It involves two translations. Translation alone can't determine similarity because there is no change in size.
2. Choice (b): It involves a translation followed by a dilation. The dilation ratio is based on [tex]$\frac{\overline{XW}}{TS}$[/tex], which doesn't align the pools to show similarity correctly.
3. Choice (c): It involves two translations, which can't demonstrate similarity on its own due to no size transformation.
4. Choice (d): This choice translates pool WXYZ so that point W aligns with point S of STUV and then uses a dilation with the ratio [tex]$\frac{\overline{TS}}{XW}$[/tex]. This process positions the pools correctly and checks their size proportions directly.
Since we are checking for similarity, which involves both positioning (using translation) and size scaling (using dilation), choice (d) is the correct approach. It effectively uses translation to overlap a vertex and verifies similarity by dilating with the appropriate ratio.
Let's analyze the statements:
- Translation: This moves a shape without altering its size or orientation. It simply slides the shape to a new location without changing its dimensions.
- Dilation: This transformation changes the size of a shape but keeps its proportions constant. If one pool is a scaled version of the other, dilation will be involved in the transformation process.
Considering the options provided, we need to identify the statement that uses the correct transformations to determine similarity:
1. Choice (a): It involves two translations. Translation alone can't determine similarity because there is no change in size.
2. Choice (b): It involves a translation followed by a dilation. The dilation ratio is based on [tex]$\frac{\overline{XW}}{TS}$[/tex], which doesn't align the pools to show similarity correctly.
3. Choice (c): It involves two translations, which can't demonstrate similarity on its own due to no size transformation.
4. Choice (d): This choice translates pool WXYZ so that point W aligns with point S of STUV and then uses a dilation with the ratio [tex]$\frac{\overline{TS}}{XW}$[/tex]. This process positions the pools correctly and checks their size proportions directly.
Since we are checking for similarity, which involves both positioning (using translation) and size scaling (using dilation), choice (d) is the correct approach. It effectively uses translation to overlap a vertex and verifies similarity by dilating with the appropriate ratio.
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