Jan. 17 HW 36: Transformations Day 1 Aim: Working with Dilation & Reflection Materials you will need for this homework: pencil ruler

There are 4 types of transformation: 1. Dilation 2. Reflection 3. Rotation 4. Translation A transformation in geometry is defined as when an object (shape) undergoes a change in position or size. Definitions:

2. Dilation A dilation is a type of transformation that changes the size of the image but the image is the same shape. To make an image smaller or larger you multiply by the scale factor. The orientation of the image is the same as the original figure.

A reflection is a kind of transformation. It is basically a “flip” of a shape over the line of reflection to create a mirror image of the shape. The image is congruent to the original shape. Orientation of the image is different from the original figure. 3. Reflection

y x   AB C D 2 A(1, -3)  A’ ________ B(3, -3)  B’________ C(2, -1)  C’________ Ex1. Dilate triangle ABC, with vertices A(1, -3), B(3, -3), and C(2, -1) with a scale factor of 2. Then write the new coordinates as A’B’C’ in the table below. A’   B’  C’ Rule for Dilation: Multiply each coordinate (x, y) by the scale factor. D2D2 Notice that the base and height of the triangles are in the ratio of 1:2

y x Ex2. Dilate rectangle BRAT, with vertices B(-6, 6), R(3, 6), A(3, 3), and T(-6, 3) with a scale factor of. Then write the new coordinates as B’R’A’T’ in the table below. B(-6, 6)  B’ ________ R(3, 6)  R’_________ A(3, 3)  A’_________ T(-6, 3)  T’_________  B  R  A  T  B’  R’  A’  T’ D Notice that the lengths and widths are in the ratio of 1:3

Ex3. Reflect Trapezoid MATH over the x-axis and label it M’A’T’H’ R over x M(1, 6)  M’_________ A(3, 6)  A’_________ T(5, 2)  T’_________ H(1, 2)  H’_________ y x M A T H Rule (Reflecting over the x-axis): (x,y)  (x, -y) M’ A’ T’ H’H’ When reflecting over the x-axis, keep the x coordinate the same and negate the y coordinate. RxRx

R over y M(1, 6)  M”_________ A(3, 6)  A” _________ T(5, 2)  T”_________ H(1, 2)  H”_________ Rule (Reflecting over the y-axis): (x,y)  (-x, y) Ex4. Reflect Trapezoid MATH over the y-axis and label it M’’A’’T’’H’’ y M A T H M” A” T” H”H” x When reflecting over the y-axis, negate the x coordinate and keep the y coordinate the same. RyRy