2022 AMC 12B Problems/Problem 5
Contents
Problem
The point is rotated counterclockwise about the point . What are the coordinates of its new position?
Solution 1 (Cartesian Plane)
is 4 units west and 3 units south of . Performing a counterclockwise rotation of , which is equivalent to a clockwise rotation of , the answer is 3 units west and 4 units north of , or .
Solution 2 (Complex numbers)
We write as We'd like to rotate about which is in the complex plane, by an angle of counterclockwise.
The formula for rotating the complex number about the complex number by an angle of counterclockwise is given as Plugging in our values , we evaluate the expression as which corresponds to on the Cartesian plane.
Video Solution 1
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See also
2022 AMC 12B (Problems • Answer Key • Resources) | |
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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