2-4 Modeling Motion with Matrices

Pre Calc A

Vocabulary

Transformations Translation Reflection Rotations Dilations

Ex 17: 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 matrixb. write the translation matrixc. use the translation matrix to find the vertices of R’S’T’U’d. Graph the pre-image and image x

y

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.

ReflectionsReflection over the: Symbolized by: Multiply the vertex matrix

by:

x-axis Rx-axis

y-axis Ry-axis

Line y=x Ry=x

10

01

10

01

01

10

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

180˚ Rot180

270˚ Rot270

01

10

10

01

01

10

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.