Transformation of Graphs Using Matrices - Rotations
A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is called the center of rotation . The amount of rotation is called the angle of rotation and it is measured in degrees.
A rotation maps every point of a preimage to an image rotated about a center point, usually the origin, using a rotation matrix.
Use the following rules to rotate the figure for a specified rotation. To rotate counterclockwise about the origin, multiply the vertex matrix by the given matrix.
Find the coordinates of the vertices of the image with after it is rotated counterclockwise about the origin.
Write the ordered pairs as a vertex matrix.
To rotate the 180° counterclockwise about the origin, multiply the vertex matrix by the rotation matrix, .
Therefore, the coordinates of the vertices of are .
Notice that the image is congruent to the preimage . Both figures have the same size and same shape.