1. 2.4 Modeling Motion in Matrices Objectives: 1.Use matrices to determine the coordinates of polygons under a given transformation.

2. 2.4 Modeling Motion in Matrices You can use simple matrices to describe motions which are called transformations. In geometry, you learned four basic transformations which are translations, reflections, rotations, and dilations. A polygon can be represented by a matrix. The x-coordinates are the first row of the matrix and the y-coordinates are the second row of the matrix. Suppose square ABCD has vertices A(-1, 3), B(3, 3), C(3, -1), and D(-1,- 1). Find the coordinates of the square after a translation of 1 unit left and 2 units down. Represent the vertices of the square ABCD as a matrix.

3. 2.4 Modeling Motion in Matrices Suppose square ABCD has vertices A(-1, 3), B(3, 3), C(3, -1), and D(-1, 1). Find the coordinates of the square after a translation of 1 unit left and 2 units down. Write the translation matrix. The translation matrix is the when added to the pre-image matrix you get the image matrix. It will have the same dimensions as the pre-image. The movement left/right is the first row and the movement up/down is the second row.

4. 2.4 Modeling Motion in Matrices Suppose square ABCD has vertices A(-1, 3), B(3, 3), C(3, -1), and D(-1, -1). Find the coordinates of the square after a translation of 1 unit left and 2 units down. Use the translation matrix to find the vertices of A’B’C’D’. This is the translated image of the square. This is A’B’C’D’. Then graph the pre-image ABCD and the image A’B’C’D’.

5. 2.4 Modeling Motion in Matrices Suppose square ABCD has vertices A(-1, 3), B(3, 3), C(3, -1), and D(-1, -1). Find the coordinates of the square after a translation of 1 unit left and 2 units down. Then graph the pre-image ABCD and the image A’B’C’D’.

6. 2.4 Modeling Motion in Matrices There are three lines over which figures are commonly reflected.

7. 2.4 Modeling Motion in Matrices Suppose square ABCD has vertices A(-1, 2), B(-4, 1), C(-3, -2), and D(0, -1). Find the image of the square after a reflection over the y-axis. First, write the vertices of the square as matrix.

8. 2.4 Modeling Motion in Matrices Suppose square ABCD has vertices A(-1, 2), B(-4, 1), C(-3, -2), and D(0, -1). Find the image of the square after a reflection over the y-axis. Choose the appropriate reflection matrix for the given reflection. Then multiple the pre-image and reflection matrix. Be careful to multiple the matrices in the correct order. This is A’B’C’D’.

9. 2.4 Modeling Motion in Matrices Suppose square ABCD has vertices A(-1, 2), B(-4, 1), C(-3, -2), and D(0, -1). Find the image of the square after a reflection over the y-axis. Then graph the pre-image ABCD and the image A’B’C’D’.

10. 2.4 Modeling Motion in Matrices There are three basic rotations about the origin for a figure.

11. 2.4 Modeling Motion in Matrices Suppose triangle PQR has vertices P(3, 2), Q(-1, 4), and R(1, -2). Find the image of the triangle after a rotation of 270° counterclockwise about the origin. First, write the vertices of the square as matrix.

12. 2.4 Modeling Motion in Matrices Choose the appropriate rotation matrix for the given rotation about the origin. Then multiple the pre-image and rotation matrix. Be careful to multiple the matrices in the correct order. This is P’Q’R’ Suppose triangle PQR has vertices P(3, 2), Q(-1, 4), and R(1, -2). Find the image of the triangle after a rotation of 270° counterclockwise about the origin.

13. 2.4 Modeling Motion in Matrices Then graph the pre-image triangle PQR and the image triangle P’Q’R’. Suppose triangle PQR has vertices P(3, 2), Q(-1, 4), and R(1, -2). Find the image of the triangle after a rotation of 270° counterclockwise about the origin.

14. Date Assignment number 93-94 11-25odd, 26 9 Read pages 98-101 for tomorrow.