This is a geometry question. ### Problem 7**Objective:** To dilate triangle $ \triangle ABC $ from center $ P $ using a scale factor of $-1$.**Solution:**1. **Identifying Points:** The given triangle $ \triangle ABC $ consists of vertices $ A $, $ B $, and $ C $. 2. **Dilation Center:** The center of dilation is point $ P $.3. **Scale Factor:** The scale factor is $-1$. **Dilation with Scale Factor $-1$:**- **Effect on Points:** Each point of the triangle will be reflected across the point $ P $ because the scale factor is $-1$. This will essentially flip the triangle across point $ P $, creating an inverted image of the original triangle where each vertex is mapped to the opposite side of $ P $ at the same distance from $ P $ as the original vertex.4. **Graphical Representation:** - The original triangle $ \triangle ABC $ is shown with vertices at points $ A $, $ B $, and $ C $. - Point $ P $ is the center of dilation, located inside the triangle. - After performing the dilation, each vertex of the triangle will be located such that: - The new position of $ A $ (let's call it $ A' $) is directly opposite to the original $ A $ with respect to $ P $. - Similarly, the positions of $ B' $ and $ C' $ will be directly opposite to the original $ B $ and $ C $ with respect to $ P $.In the diagram:- The original triangle is indicated with vertices $ A $, $ B $, and $ C $.- Point $ P $ is displayed to the left of triangle $ \triangle ABC $.- The dilated triangle is not explicitly shown, but it would be reflected through $ P $ considering the equal distance and opposite direction from $ P $.

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Answered: 7. Dilate AABC from center P using a…

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7. Dilate AABC from center P using a scale factor of -1. I B

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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This is a geometry question.

### Problem 7

**Objective:** To dilate triangle $ \triangle ABC $ from center $ P $ using a scale factor of $-1$.

**Solution:**
1. **Identifying Points:** The given triangle $ \triangle ABC $ consists of vertices $ A $, $ B $, and $ C $.
2. **Dilation Center:** The center of dilation is point $ P $.
3. **Scale Factor:** The scale factor is $-1$.

**Dilation with Scale Factor $-1$:**
- **Effect on Points:** Each point of the triangle will be reflected across the point $ P $ because the scale factor is $-1$. This will essentially flip the triangle across point $ P $, creating an inverted image of the original triangle where each vertex is mapped to the opposite side of $ P $ at the same distance from $ P $ as the original vertex.

4. **Graphical Representation:**
- The original triangle $ \triangle ABC $ is shown with vertices at points $ A $, $ B $, and $ C $.
- Point $ P $ is the center of dilation, located inside the triangle.
- After performing the dilation, each vertex of the triangle will be located such that:
- The new position of $ A $ (let's call it $ A' $) is directly opposite to the original $ A $ with respect to $ P $.
- Similarly, the positions of $ B' $ and $ C' $ will be directly opposite to the original $ B $ and $ C $ with respect to $ P $.

In the diagram:
- The original triangle is indicated with vertices $ A $, $ B $, and $ C $.
- Point $ P $ is displayed to the left of triangle $ \triangle ABC $.
- The dilated triangle is not explicitly shown, but it would be reflected through $ P $ considering the equal distance and opposite direction from $ P $.

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