Answered: Rotate the point (2,5) by (3/5,4/5)…

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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Question

Rotate the point (2,5) by (3/5,4/5) around origin (0,0).

Expert Solution

Step 1: Given information

$G i v e n : p o i n t A (2, 5) R o t a t e b y (\frac{3}{5}, \frac{4}{5}) a r o u n d o r i g i n (0, 0) .$

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Method:

Find the angle of rotation.

Use Rotation matrix, R for anticlockwise rotation of the given point (x, y) by angle $θ$ , around origin (0, 0)

$\begin{array}{rcl} [\begin{matrix} x' \\ y' \end{matrix}] & = & R_{θ} [\begin{matrix} x \\ y \end{matrix}] \\ W h e r e, \end{array} R_{θ} = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]$

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