GATE Overflow Test Series | Spatial and Analytical Aptitude | Test 1 | Question: 17

Question

The image of the point $(-21,-19)$ under a rotation by $35730^\circ$ about the origin is given by

• A. $(-19,21)$
• B. $(21,-19)$
• C. $(19,-21)$
• D. $(-21,19)$

Answer 1

A rotation by $35730^\circ$ is the same as ninety-nine consecutive rotations by $360^\circ$ followed by a rotation by $90^\circ\: \text{(because}\:\: 35730 = 99 \cdot 360 + 90)$.

A rotation by $360^\circ$ maps every point onto itself. In other words, it doesn't change anything.

So a rotation by $35730^\circ$ is the same as a rotation by $90^\circ$. Therefore, we can simply use the pattern $R_{(0,0),90^\circ}(x,y)=(-y,x).$

$R_{(0,0),90^\circ}(-21,-19)=(19,-21).$

$\therefore R_{(0,0),35730^\circ}(-21,-19)=(19,-21).$

So, the correct answer is $(C).$

Reference: http://jwilson.coe.uga.edu/EMAT6680/Adcock/Adcock6690/RLAInstructUnit1/RLATrigLesson1.htm

Comments

Thank you

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Lakshman Patel RJIT

what about 90 degree clockwise rotation.how the co-ordinates will change

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$R_{(0,0),-90^\circ}(x,y)=(y,-x).$

For more info see here https://www.math-only-math.com/90-degree-clockwise-rotation.html

Answer 2

In computer graphics we have 1 formula → https://www.geeksforgeeks.org/2d-transformation-rotation-objects/

so, at angle of 90 degree

[x’] = [0 -1][x]

[y’] = [1  0][y]

result in (19,21)