1. Which of the following show the correct angle and direction of rotation for the figure below? 270° clockwise 90° clockwise 180°clockwise 90° counterclockwise R Q 'S' R $
1. Which of the following show the correct angle and direction of rotation for the figure below? 270° clockwise 90° clockwise 180°clockwise 90° counterclockwise R Q 'S' R $
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hello can you help me with this problem? Which of the following show the correct angle and direction of rotation for the figure below?
Transcribed Image Text:### Rotation of Figures in a Coordinate Plane
#### Question 1:
Which of the following show the correct angle and direction of rotation for the figure below?
#### Image Description:
A coordinate plane featuring a triangle with its vertices labeled as \( Q \), \( R \), and \( S \). The figure is rotated around the origin. The rotated figure has its vertices labeled as \( Q' \), \( R' \), and \( S' \).
#### Answer Choices:
- \( \circ \) 270° clockwise
- \( \circ \) 90° clockwise
- \( \circ \) 180° clockwise
- \( \circ \) 90° counterclockwise
### Explanation:
The coordinate plane shows two triangles:
1. The original triangle \( QRS \) positioned in the first quadrant.
2. The rotated triangle \( Q'R'S' \) positioned in the fourth quadrant.
#### Analysis of Rotation:
- The rotation appears to be around the origin (0,0).
- When rotating a figure:
- 90° clockwise rotation moves a point (x, y) to (y, -x).
- 180° clockwise rotation moves a point (x, y) to (-x, -y).
- 270° clockwise rotation (equivalent to 90° counterclockwise) moves a point (x, y) to (-y, x).
By examining the positions:
- \( Q(x1, y1) \) has moved to \( Q’(y1, -x1) \) indicating a 90° clockwise rotation.
Hence, the correct answer is:
- \( \circ \) 90° clockwise
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