How to Graph Transformation on the Coordinate Plane: Rotation?

How to graph transformation on the coordinate plane: rotation, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

• For rotating a shape (90) degrees counterclockwise:((x, y)→(-y, x))
• For rotating a shape (180) degrees: ((x, y)→(-x, -y))
• For rotating a shape (270) degrees counterclockwise: ((x, y)→(y, -x))

• You should be able to assume the center of rotation to be the origin when working on the coordinate plane unless otherwise stated.
• You should be able to assume that, unless otherwise stated, a positive angle of rotation rotates the figure counterclockwise and a negative angle rotates it clockwise.
• You need to be able to recognize angles of certain sizes when working with rotation. ((90^{circ}, 180^{circ}, 270^{circ}, …))
• You must be able to understand the directionality of a unit circle. (the circle with a radius length of (1) unit)
• You must know that rotation on a coordinate grid is considered to be counterclockwise unless otherwise stated.

Transformation: Rotation, Example 1:

Transformation: Rotation, Example 2:

Solution:

The rule for rotating a shape (270) degrees is ((x, y)→(y, -x))

(A=(-4, 1)→A^prime=(1, 4))

(B=(-3, 3)→B^prime=(3, 3))

(C=(-1, 4)→C^prime=(4, 1))

(D=(0, 2)→D^prime=(2, 0))

(C=(-2, 1)→C^prime=(1, 2))

Graph the figure (ABCDE) and its image (A^prime B^prime C^prime D^prime E^prime).

Exercises for Transformation: Rotation

Graph the image of the figure using the transformation given.

1.(color{blue}{Rotation 180^{circ}})

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2.(color{blue}{Rotation 90^{circ}})

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