4.1.3 Using Matrices to Transform Geometric Figures Key Objectives • Use matrices to transform plane figures. Key Terms • A dilation is a transformation that changes the size, but not the shape, of a figure. • A reduction , or contraction, is a dilation with a scale factor greater than 0 but less than 1. The position, shape, and size of a polygon on a coordinate plane can be described by naming the ordered pairs that define the polygon’s vertices. A polygon on a coordinate plane can also be described by a matrix, called a coordinate matrix, where the entries from each column are the coordinates of a vertex (the entries of the first row are the x -coordinates of the polygon’s vertices and the entries of the second row are the y -coordinates of the polygon’s vertices). Example 1 Using Matrices to Translate a Figure A translation matrix is a matrix used to translate coordinates on a coordinate plane. The matrix sum of a preimage and a translation matrix gives the coordinates of the translated image.
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