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Rotations about the Origin

High School Math based on the topics required for the Regents Exam conducted by NYSED.

When working in the coordinate plane, assume the center of rotation to be the origin unless told otherwise.

A positive angle of rotation turns the figure counterclockwise, and a negative angle of rotation turns the figure in a clockwise direction.

Rotation of 90 degrees

R(x, y) = (–y, x)

Rotation of 180 degrees (same as point reflection in the origin)

R(x, y) = (–x, –y)

Rotation of 270 degrees (same as rotation of –90 degrees)

R(x, y) = (y , –x)

Rotate 90 degrees
Rotating a polygon around the origin.

This tutorial shows why all signs of an ordered pair of an object become opposite when rotating that object 180 degrees around the origin.

Graphing and Describing Rotations
Rotate 90 degrees counter-clockwise.
How to Rotate a Shape About the Origin 90° Counter-Clockwise.


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