# Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

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Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

* A transformation is a change made to a figure. * The original figure is called the preimage (A), while the transformed figure is called the image (A’). * When we slide a figure without changing the size or shape of the figure, it is said to be a translation. * By using matrix addition, we can translate the vertices of a figure.

Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), translate the preimage 5 units right and 3 units down. Then, sketch the image.

Quadrilateral ABCD has vertices A(0,0), B(-2,5), C(2,3) and D(4.1). Use a matrix to find the coordinates of the vertices of the image translated 5 units left and 2 units up. Then graph ABCD and A’B’C’D’.

* A dilation is a transformation that changes the size of a figure. EXAMPLE: Given triangle ABC where A (–5,0), B (8,-1) and C (4,5) Find the coordinates of each image under the following dilations. Then graph the images.: a.) 4 b.) 1/5c.) -1.5

* A reflection, or flip, is a transformation that creates symmetry on the coordinate plane. * You can use matrix multiplication to graph reflections in the coordinate plane. * A rotation is a transformation that turns a figure about a fixed point called a center of rotation. * You can rotate a figure as much as 360 degrees. In this text, all rotations are counterclockwise about the origin.

Matrices for Reflections in the Coordinate Plane Reflection in the y-axis Reflection in the x-axis Reflection in the line y = x Reflection in the line y = –x

Matrices for Rotations in the Coordinate Plane Rotation of 90°Rotation of 180° Rotation of 270° Rotation of 360°

* EXAMPLE: Given triangle ABC where A (-3,0), B (– 4,4) and C (1,1). Reflect the triangle across the y-axis, x-axis, y=x and y = -x. Then, sketch the image.

* EXAMPLE: Given quadrilateral ABCD where A (1, 1), B (3,1), C (6,4),and D(1,3). Rotate the quadrilateral: a.) 90 ° b.) 180° c.) 270° d.) 360° Then, sketch the image.

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