Topics 3.6-3.9: Rotations 9. Consider the following coordinate plane. Part A: Sketch the polygon SUMO with vertices at S(10. -4), U (6, –5). M(4, 1), 0(8, 2) in the coordinate plane above. Part B: Rotate SUMO 270° counterclockwise about the origin. What are the coordinates of S'U'M'O'?

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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**Topic 3.6-3.9: Rotations**

**9. Consider the following coordinate plane.**

**Part A:** Sketch the polygon **SUMO** with vertices at \( S(10, -4), U(6, -5), M(4, 1), O(8, 2) \) in the coordinate plane above.

**Part B:** Rotate **SUMO** \(270^\circ\) counterclockwise about the origin. What are the coordinates of \( S'U'M'O' \)?

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**Graph Explanation:**

The graph is a standard coordinate plane with a grid. The x-axis and y-axis are labeled, and the plane extends from -10 to 10 on both axes. The vertices of the polygon **SUMO** need to be plotted on this plane according to the given coordinates.

After plotting, a \(270^\circ\) counterclockwise rotation about the origin will involve repositioning each vertex to new coordinates. 

To perform this rotation mathematically:
- For each point \((x, y)\), the new position after a \(270^\circ\) counterclockwise rotation will be \((y, -x)\).

Apply this formula to find the new coordinates of \( S'U'M'O' \).
Transcribed Image Text:**Topic 3.6-3.9: Rotations** **9. Consider the following coordinate plane.** **Part A:** Sketch the polygon **SUMO** with vertices at \( S(10, -4), U(6, -5), M(4, 1), O(8, 2) \) in the coordinate plane above. **Part B:** Rotate **SUMO** \(270^\circ\) counterclockwise about the origin. What are the coordinates of \( S'U'M'O' \)? --- **Graph Explanation:** The graph is a standard coordinate plane with a grid. The x-axis and y-axis are labeled, and the plane extends from -10 to 10 on both axes. The vertices of the polygon **SUMO** need to be plotted on this plane according to the given coordinates. After plotting, a \(270^\circ\) counterclockwise rotation about the origin will involve repositioning each vertex to new coordinates. To perform this rotation mathematically: - For each point \((x, y)\), the new position after a \(270^\circ\) counterclockwise rotation will be \((y, -x)\). Apply this formula to find the new coordinates of \( S'U'M'O' \).
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