Section 3: Using Matrices to Transform Geometric Figures

UUse matrices to transform a plane figure.

ttranslation matrix rreflection matrix rrotation matrix

AArtists, such as M. C. Escher, may use repeated transformed patterns to create their work. (See Exercise 16.)

YYou can describe the position, shape, and size of a polygon on a coordinate plane by naming the ordered pairs that define its vertices. TThe coordinates of TRIABC below are A (-2, -1), B (0, 3), and C (1, -2). YYou can also define TRIABC by a matrix:

AA translation matrix is a matrix used to translate coordinates on the coordinate plane. TThe matrix sum of a preimage and a translation matrix gives the coordinates of the translated image.

AA dilation is a transformation that scales—enlarges or reduces—the preimage, resulting in similar figures. RRemember that for similar figures, the shape is the same but the size may be different. Angles are congruent, and side lengths are proportional. WWhen the center of dilation is the origin, multiplying the coordinate matrix by a scalar gives the coordinates of the dilated image. IIn this lesson, all dilations assume that the origin is the center of dilation.

AA reflection matrix is a matrix that creates a mirror image by reflecting each vertex over a specified line of symmetry. TTo reflect a figure across the y-axis, multiply f by the coordinate matrix. TThis reverses the x-coordinates and keeps the y-coordinates unchanged.

AA rotation matrix is a matrix used to rotate a figure. Example 4 gives several types of rotation matrices.

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