Use the accompanying grid to answer this question. 5. a. Triangle RST has coordinates R(-1, 3), S(3, 1), and T(0, 8). Plot triangle ABC the image of triangle RST after the transformation T c. Plot triangle A"B"C", the result of the transformation R 90 of triangle A'B'C'. 4, 2 b. Plot triangle A'B'C' the image of triangle ABC after the transformation r d. What single transformation would map triangle ABC to triangle A'B'C".

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
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### Geometry Transformations Educational Exercise

**5. Use the accompanying grid to answer this question.**

**a.** Triangle RST has coordinates R(-1, 3), S(3, 1), and T(0, 8). Plot triangle ABC, the image of triangle RST after the transformation \( T_{4,2} \). 

**b.** Plot triangle A'B'C’, the image of triangle ABC after the transformation \( r_{y=x} \).

**c.** Plot triangle A''B''C'', the result of the transformation \( R_{90^\circ} \) of triangle A’B’C’.

**d.** What single transformation would map triangle ABC to triangle A''B''C''?

**Explanation:**

The exercise involves transforming a triangle using different operations on a coordinate grid. The steps involve plotting initial points, translating them, reflecting over the line \( y = x \), and rotating them. 

**Grid:**

The accompanying grid for plotting transformations is a Cartesian plane with:

- The x-axis and y-axis each marked with units.
- Arrows indicating positive directions on both axes.
- The origin (0, 0) at the center.
  
Students will use this grid to plot points and visualize transformations step-by-step.
Transcribed Image Text:### Geometry Transformations Educational Exercise **5. Use the accompanying grid to answer this question.** **a.** Triangle RST has coordinates R(-1, 3), S(3, 1), and T(0, 8). Plot triangle ABC, the image of triangle RST after the transformation \( T_{4,2} \). **b.** Plot triangle A'B'C’, the image of triangle ABC after the transformation \( r_{y=x} \). **c.** Plot triangle A''B''C'', the result of the transformation \( R_{90^\circ} \) of triangle A’B’C’. **d.** What single transformation would map triangle ABC to triangle A''B''C''? **Explanation:** The exercise involves transforming a triangle using different operations on a coordinate grid. The steps involve plotting initial points, translating them, reflecting over the line \( y = x \), and rotating them. **Grid:** The accompanying grid for plotting transformations is a Cartesian plane with: - The x-axis and y-axis each marked with units. - Arrows indicating positive directions on both axes. - The origin (0, 0) at the center. Students will use this grid to plot points and visualize transformations step-by-step.
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