2022 AMC 12B Problems/Problem 5

Revision as of 19:49, 19 November 2022 by Thestudyofeverything (talk | contribs) (Solution 1)

Problem

The point $(-1, -2)$ is rotated $270^{\circ}$ counterclockwise about the point $(3, 1)$. What are the coordinates of its new position?

$\textbf{(A)}\ (-3, -4) \qquad \textbf{(B)}\ (0,5) \qquad \textbf{(C)}\ (2,-1) \qquad \textbf{(D)}\ (4,3) \qquad \textbf{(E)}\ (6,-3)$

Solution 1

$(-1,-2)$ is 4 units west and 3 units south of $(3,1)$. Performing a counterclockwise rotation of $270^{\circ}$, which is equivalent to a clockwise rotation of $90^{\circ}$, the answer is 3 units west and 4 units north of $(3,1)$, or $\boxed{\textbf{(B)}\ (0,5)}$.

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Video Solution 1

https://youtu.be/L09yN1Y5CBI

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See also

2022 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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