1. [ ] [ ] EXAMPLE 4 Use scalar multiplication in a dilation
The vertices of quadrilateral KLMN are K(– 6, 6), L(– 3, 6), M(0, 3), and N(– 6, 0). Use scalar multiplication to find the image of KLMN after a dilation with its center at the origin and a scale factor of Graph KLMN and its image. 1 3
SOLUTION
[ ] 1 3
– 6 – – 6
K L M N
Scale factor
Polygon matrix
[ ] =
– 2 – – 2
K’ L’ M’ N’
Image matrix

2. EXAMPLE 5
Find the image of a composition
The vertices of ABC are A(– 4, 1), B(– 2, 2), and C( – 2, 1). Find the image of ABC after the given composition.
Translation: (x, y)
(x + 5, y + 1)
Dilation: centered at the origin with a scale factor of 2
SOLUTION
STEP 1
Graph the preimage ABC on the coordinate plane.

3. EXAMPLE 5
Find the image of a composition
STEP 2
Translate ABC 5 units to the right and 1 unit up. Label it A’B’C’.
STEP 3
Dilate A’B’C’ using the origin as the center and a scale factor of 2 to find A”B”C”.

4. GUIDED PRACTICE
for Examples 4 and 5 5.
The vertices of RST are R(1, 2), S(2, 1), and T(2, 2). Use scalar multiplication to find the vertices of R’S’T’ after a dilation with its center at the origin and a scale factor of 2.
R’(2,4), S’(4,2), T’(4,4)
ANSWER

5. GUIDED PRACTICE
for Examples 4 and 5 6.
A segment has the endpoints C( –1, 1) and D(1, 1). Find the image of CD after a 90° rotation about the origin followed by a dilation with its center at the origin and a scale factor of 2.
ANSWER
C’( 2, 2), D’( 2,2)