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Rotations about the Origin

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

In this lesson, we will look at rotation in the coordinate plane where the center of rotation is at the origin.

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

The following figures show rotation of 90°, 180°, and 270° about the origin and the relationships between the points in the source and the image. Scroll down the page for more examples and solutions on rotation about the origin in the coordinate plane.

Rotation about the Origin

Rotate 90 degrees
Rotating a polygon around the origin.
For a 90 degree rotation around the origin, switch the x,y values of each ordered pair for the location of the new point.

How to rotate an object 180 degrees 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.
Draw an image of a polygon with vertices A(2,2), B(4,3), C(4,5) and D(1,4). Graph the image of quadrilateral ABCD after a rotation 90° counterclockwise about the origin and write the coordinates of the vertices. How to Rotate a Shape About the Origin 90° Counter-Clockwise?
Step 1: Find the points of the vertices.

Step 2: Switch the x and y values for each point.

Step 3: Multiply the new x-values by -1.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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