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Rotations review

Review the basics of rotations, and then perform some rotations.

What is a rotation?

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
For example, this animation shows a rotation of pentagon IDEAL about the point (0,1). You can see the angle of rotation at the bottom, which increases the further we rotate the figure from its original position.
An XY coordinate plane with 1 pentagon graphed. The horizontal x axis runs left to right from negative 10 to 10 in intervals of 1. The vertical y axis runs up and down from negative 10 to 10 in intervals of 1. The pentagon has 5 vertices. Point D is plotted at (0, negative 1), point E is plotted at (3, 4), point A is plotted at (7, 5), point L is plotted at (7, negative 3), and point I is plotted at (negative 3, negative 5). There is a video that shows the figure being rotated counterclockwise about (0, negative 1). The video shows the figure every 15 degrees that it is rotated.
The result of a rotation is a new figure, called the image. The image is congruent to the original figure.
Want to learn more about different types of transformations? Check out this video.

Performing rotations

Although a figure can be rotated any number of degrees, the rotation will usually be a common angle such as 45or 180.
If the number of degrees are positive, the figure will rotate counter-clockwise.
If the number of degrees are negative, the figure will rotate clockwise.
The figure can rotate around any given point.
Example:
Rotate OAR 60 about point (2,3).
The center of rotation is (2,3).
An XY coordinate plane with 1 triangle graphed. The horizontal x axis runs left to right from negative 10 to 10 in intervals of 1. The vertical y axis runs up and down from negative 10 to 10 in intervals of 1. The triangle has 3 vertices. Point O is plotted at (approximately 2.5, 1), point A is plotted at (approximately 8.5, negative 1.5), and point R is plotted at (approximately 2.5, negative 4). There is a solid point plotted at (negative 2, negative 3) that is the center of rotation for the figure.
Rotation by 60 moves each point about (2,3) in a counter-clockwise direction. The rotation maps OAR onto the triangle below.
An XY coordinate plane with a triangle and a rotated copy of it graphed. The horizontal x axis runs left to right from negative 10 to 10 in intervals of 1. The vertical y axis runs up and down from negative 10 to 10 in intervals of 1. The triangle is rotated to the left of center. The original triangle has 3 vertices. Point O is plotted at (approximately 2.5, 1), point A is plotted at (approximately 8.5, negative 1.5), and point R is plotted at (approximately 2.5, negative 4). The vertices of the rotated triangle are (approximately 3.25, 3), (2, approximately 6.75), and (approximately 1.25, approximately 0.50). There is a solid point plotted at (negative 2, negative 3) that is the center of rotation for the figure.
Want to learn more about performing rotations? Check out this video.

Practice

Problem 1
NOW is rotated 90 about the origin.
Draw the image of this rotation.

Want to try more problems like this? Check out this exercise.

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