Geometric Transformations

1
Section 4.4

• Geometric Transformations

2
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
(For help, go to Lesson 2-6.)
Check Skills Youll Need
4-4
3
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
1. y x 2 left 4 units y x 6 
Solutions
2. (x) x 2 up 5 units (x) x 7
3. g(x) x right 3 units g(x) x 3 
4. y x down 2 units y x 2
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4
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
5. y x 3 down 2 units y x
3 2
Solutions (continued)
1 3
6. (x) 2x right 2 units (x) 2x 4
1 3
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5
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
Triangle ABC has vertices A(1, 2), B(3, 1) and
C(2, 3). Use a matrix to find the vertices of the
image translated 3 units left and 1 unit up.
Graph ABC and its image A?B?C?.
The coordinates of the vertices of the image
are A? (2, 1), B? (0, 2), C? (1, 4).
Quick Check
4-4
6
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
2 3
The figure in the diagram is to be reduced by a
factor of . Find the coordinates of the
vertices of the reduced figure.
Write a matrix to represent the coordinates of
the vertices.
Quick Check
4-4
7
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
Reflect the triangle with coordinates A(2, 1),
B(3, 0), and C(4, 2) in each line. Graph
triangle ABC and each image on the same
coordinate plane.
a. x-axis
b. y-axis
c. y x
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8
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
(continued)
d. y x
Quick Check
4-4
9
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
Rotate the triangle from Additional Example 3 as
indicated. Graph the triangle ABC and each image
on the same coordinate plane.
a. 90?
b. 180?
c. 270?
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10
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
(continued)
d. 360?
Quick Check
4-4
11
Geometric Transformations with Matrices
ALGEBRA 2 LESSON 4-4
For these questions, use triangle ABC with
vertices A(1, 1), B(2, 2), and C(1, 2).
1. Write a matrix equation that represents a
translation of triangle ABC 7 units left and
3 units up. 2. Write a matrix equation that
represents a dilation of triangle ABC with a
scale factor of 5. 3. Use matrix
multiplication to reflect triangle ABC in
the line y x. Then draw the preimage and
image on the same coordinate plane.
4-4