We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine whether pool STUV is similar to pool WXYZ, we need to look at geometric transformations that can map one shape onto the other. Two key transformations used to establish similarity are translation and dilation.
Let's explore the options:
1. Translate WXYZ so that point [tex]$W$[/tex] of WXYZ lies on point [tex]$S$[/tex] of STUV, then translate WXYZ so that point [tex]$X$[/tex] of WXYZ lies on point [tex]$T$[/tex] of STUV.
- This involves translating the shape twice, but there is no dilation mentioned here. Without a dilation, we cannot confirm similarity because similarity requires proportional resizing, not just repositioning.
2. Translate WXYZ so that point [tex]$X$[/tex] of WXYZ to point [tex]$T$[/tex] of STUV, then dilate WXYZ by the ratio [tex]$\frac{\overline{XW}}{TS}$[/tex].
- This involves translating first and then dilating using the ratio of corresponding side lengths. This keeps the corresponding angles equal and scales the sides proportionally, which establishes similarity.
3. Translate WXYZ so that point [tex]$X$[/tex] of WXYZ.
- This option is incomplete and does not provide enough information to assess similarity.
4. Translate WXYZ so that point [tex]$W$[/tex] of WXYZ lies on point [tex]$S$[/tex] of STUV, then dilate WXYZ by the ratio [tex]$\frac{\overline{TS}}{XW}$[/tex].
- This involves translating first and then dilating by a specific ratio. The ratio given here effectively scales WXYZ to match the proportional dimensions of STUV. This is a correct approach to establish similarity.
Therefore, the correct approach involves translating and appropriately scaling one shape to match the other. Translating the point and then dilating by a specific ratio matches the necessary conditions for similarity of the two pools. In this context, option 4 correctly describes the process needed to determine similarity between pool STUV and pool WXYZ.
Let's explore the options:
1. Translate WXYZ so that point [tex]$W$[/tex] of WXYZ lies on point [tex]$S$[/tex] of STUV, then translate WXYZ so that point [tex]$X$[/tex] of WXYZ lies on point [tex]$T$[/tex] of STUV.
- This involves translating the shape twice, but there is no dilation mentioned here. Without a dilation, we cannot confirm similarity because similarity requires proportional resizing, not just repositioning.
2. Translate WXYZ so that point [tex]$X$[/tex] of WXYZ to point [tex]$T$[/tex] of STUV, then dilate WXYZ by the ratio [tex]$\frac{\overline{XW}}{TS}$[/tex].
- This involves translating first and then dilating using the ratio of corresponding side lengths. This keeps the corresponding angles equal and scales the sides proportionally, which establishes similarity.
3. Translate WXYZ so that point [tex]$X$[/tex] of WXYZ.
- This option is incomplete and does not provide enough information to assess similarity.
4. Translate WXYZ so that point [tex]$W$[/tex] of WXYZ lies on point [tex]$S$[/tex] of STUV, then dilate WXYZ by the ratio [tex]$\frac{\overline{TS}}{XW}$[/tex].
- This involves translating first and then dilating by a specific ratio. The ratio given here effectively scales WXYZ to match the proportional dimensions of STUV. This is a correct approach to establish similarity.
Therefore, the correct approach involves translating and appropriately scaling one shape to match the other. Translating the point and then dilating by a specific ratio matches the necessary conditions for similarity of the two pools. In this context, option 4 correctly describes the process needed to determine similarity between pool STUV and pool WXYZ.
Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
