4­4 Geometric Transformations with Matrices
Objective
Represent translations and dilations with matrices.
Title: Nov 1­4:16 PM (1 of 10)
Check Skills You'll Need
Without using graphing technology, graph each function and its translation.
Write the new function.
1. y = x + 2; left 4 units
2. y = x; down 2 units
3. f(x) = |x ­ 3|; down 2 units
Title: Nov 1­4:30 PM (2 of 10)
You can write the vertices of a figure as a matrix.
For example, the matrix below represents the vertices of figure ABCD.
Title: Nov 1­4:43 PM (3 of 10)
A change made to a figure is a TRANSFORMATION
of the figure. The transformed figure is the IMAGE.
The original figure is the PREIMAGE.
There are two types of transformations
that we will work with.
Title: Nov 1­4:40 PM (4 of 10)
Translation
Dilation
Title: Nov 1­4:52 PM (5 of 10)
TRANSLATION
Graph both quadrilaterals
Title: Nov 1­5:24 PM (6 of 10)
You try!
Translate the Pentagon with vertices (0, ­5), (­1, ­1), (­5, 0), (1, 3), and (4, 0)
3 units left and 2 units up. Graph the pre­image and the image.
Title: Nov 1­7:00 PM (7 of 10)
DILATION
Title: Nov 1­5:28 PM (8 of 10)
YOU TRY!
The coordinates of the vertices of figure ABC are A(­5, 0), B(8, ­1), and C(4, 5). Find the coordinates of the image if it is dilated with a scale factor of ­1.5.
Title: Nov 1­7:05 PM (9 of 10)
HOMEWORK
p. 195 #1­9, 27­30,
57, 60, 61 Title: Nov 1­5:55 PM (10 of 10)