Lesson 2-4

Example 1
Suppose triangle ABC with vertices A(-3, 1), B(1, 4), and C(-1, -2) is translated 2 units right and 3 units down.

a.	Represent the vertices of the triangle as a matrix.

b.	Write the translation matrix.

c.	Use the translation matrix to find the vertices of A’B’C’, the translated image of the triangle.

d.	Graph triangle ABC and its image.

a.	The matrix representing the coordinates of the vertices of triangle ABC will be a 2  3 matrix.

b.	The translation matrix is .

c.	Add the two matrices.

d.	Graph the points represented	
by the resulting matrix.

	

Example 2
ANIMATION  To create an image that appears to be reflected in a mirror, an animator
will use a matrix to reflect an image over the y-axis. Use a reflection matrix to find the coordinates of the vertices of a parallelogram reflected in a mirror (the y-axis) if the coordinates of the points connected to create the parallelogram are (-4, 3), (2, 3), (-1, -2),
and (-7, -2).

First, write the vertex matrix for the points used to define the parallelogram.

Multiply by the y-axis reflection matrix.

The vertices used to define the reflection are (4, 3), (-2, 3), (1, -2), and (7, -2).

	

Example 3
ANIMATION  Suppose a figure is animated to spin around a certain point. Numerous rotation images would be necessary to make a smooth movement image. If the image has key points at (2, 1), (4, 2), and (3, 5) and the rotation is about the origin, find the location of these points at the 90, 180, and 270 counterclockwise rotations.

First write the vertex matrix. Then multiply it by each rotation matrix.
The vertex matrix is .

Rot90	

Rot180	

Rot270	

	

Example 4
A trapezoid has vertices at A(2, 3), B(-3, 3), C(-5, -2), and D(3, -2). Find the coordinates of the dilated trapezoid ABCD for a scale factor of 2. Describe the dilation.

First write the coordinates of the vertices as a matrix. Then do a scalar multiplication using the scale factor.

2
The vertices of the image are A(4, 6),	
B(-6, 6), C(-10, -4), and D(6,-4).

The image has sides that are twice
the length of the original figure.