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if th SOLUTION we Apply It 1 Khadija draws AABC in the coordinate -2 plane. She dilates AABC using a scale factor of with the center of dilation at the origin to form AA'B'C'.Then she dilates A AA'B'C' using a scale factor of vith a center of dilation at the origin to form AA"B"C". What are the coordinates of AA"B"C"? Show your work. SOLUTION LESSON 5 Perform and Descr

if th SOLUTION we Apply It 1 Khadija draws AABC in the coordinate -2 plane. She dilates AABC using a scale factor of with the center of dilation at the origin to form AA'B'C'.Then she dilates A AA'B'C' using a scale factor of vith a center of dilation at the origin to form AA"B"C". What are the coordinates of AA"B"C"? Show your work. SOLUTION LESSON 5 Perform and Descr

Elementary Geometry For College Students, 7e
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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### Dilation of Triangle \( \triangle ABC \) on the Coordinate Plane #### Problem Statement Khadija draws \( \triangle ABC \) in the coordinate plane. She dilates \( \triangle ABC \) using a scale factor of \(\frac{1}{2}\) with the center of dilation at the origin to form \( \triangle A'B'C' \). She then dilates \( \triangle A'B'C' \) using a scale factor of \(\frac{3}{2}\) with the center of dilation at the origin to form \( \triangle A''B''C'' \). **Task:** What are the coordinates of \( \triangle A''B''C'' \)? Show your work. #### Explanation of the Graph - The graph is a coordinate plane with lines marked for both x and y axes. - \( \triangle ABC \) is plotted with vertices at specific coordinates. The side lengths and orientation of the triangle are visible. #### Steps to Solve 1. **Dilate \( \triangle ABC \) with scale factor \( \frac{1}{2} \):** - Each coordinate of \( \triangle ABC \) is multiplied by \( \frac{1}{2} \) to get \( \triangle A'B'C' \). 2. **Dilate \( \triangle A'B'C' \) with scale factor \( \frac{3}{2} \):** - Each coordinate of \( \triangle A'B'C' \) is multiplied by \( \frac{3}{2} \) to get \( \triangle A''B''C'' \). #### Solution **Calculate the coordinates for each step and obtain the final coordinates for \( \triangle A''B''C'' \).** - Verify and confirm the steps mathematically to ensure accuracy in plotting the triangles and obtaining the coordinates.
Transcribed Image Text:### Dilation of Triangle \( \triangle ABC \) on the Coordinate Plane #### Problem Statement Khadija draws \( \triangle ABC \) in the coordinate plane. She dilates \( \triangle ABC \) using a scale factor of \(\frac{1}{2}\) with the center of dilation at the origin to form \( \triangle A'B'C' \). She then dilates \( \triangle A'B'C' \) using a scale factor of \(\frac{3}{2}\) with the center of dilation at the origin to form \( \triangle A''B''C'' \). **Task:** What are the coordinates of \( \triangle A''B''C'' \)? Show your work. #### Explanation of the Graph - The graph is a coordinate plane with lines marked for both x and y axes. - \( \triangle ABC \) is plotted with vertices at specific coordinates. The side lengths and orientation of the triangle are visible. #### Steps to Solve 1. **Dilate \( \triangle ABC \) with scale factor \( \frac{1}{2} \):** - Each coordinate of \( \triangle ABC \) is multiplied by \( \frac{1}{2} \) to get \( \triangle A'B'C' \). 2. **Dilate \( \triangle A'B'C' \) with scale factor \( \frac{3}{2} \):** - Each coordinate of \( \triangle A'B'C' \) is multiplied by \( \frac{3}{2} \) to get \( \triangle A''B''C'' \). #### Solution **Calculate the coordinates for each step and obtain the final coordinates for \( \triangle A''B''C'' \).** - Verify and confirm the steps mathematically to ensure accuracy in plotting the triangles and obtaining the coordinates.
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