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2-4 Modeling Motion with Matrices Pre Calc A Vocabulary Transformations Translation Reflection Rotations Dilations Ex 17: y Suppose quadrilateral RSTU with vertices R(3, 2), S(7, 4), T(9, 8) and U(5, 6) is translated 2 units right and 3 units down. a. represent the vertices of the quadrilateral as a matrix b. write the translation matrix c. use the translation matrix to find the vertices of R’S’T’U’ d. Graph the pre-image and image Ex : A parallelogram has vertices W(-2, 4), X(0, 8), Y(4, 6), and Z(2, 2). Find the coordinates of the dialted parallelogram W’X’Y’Z’ for a scale factor of 1.5. Describe the dilation. Reflections Reflection over the: Symbolized by: Multiply the vertex matrix by: x-axis Rx-axis 1 0 0 1 y-axis Ry-axis 1 0 0 1 Line y=x Ry=x 0 1 1 0 Ex : A triangle has vertices A(-1, 2), B(4, 4) and C(3, -2). Find the image of the triangle after a reflection over the y-axis. Rotations: For a counterclockwise rotation about the origin: Symbolized by: Multiply the vertex matrix by: 90˚ Rot90 0 1 1 0 180˚ Rot180 1 0 0 1 270˚ Rot270 0 1 1 0 Ex last one: A triangle has vertices A(-1, 2), B(4, 4) and C(3, -2). Find the image of the triangle after a rotation of 90˚ about the origin.