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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.
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.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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