1. Geometry
Section 9.7

3. EXAMPLE 1
Identify dilations
Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. a.
SOLUTION a.
Because = , the scale factor is k =
The image P’ is an enlargement.
CP’ CP 12 8 3 2

4. EXAMPLE 1
Identify dilations
Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. b.
SOLUTION
Because = , the scale factor is k =
The image P’ is a reduction.
CP’ CP 18
30’ 3 5 b.

5. EXAMPLE 2
Draw a dilation
Draw and label DEFG. Then construct a dilation of DEFG with point D as the center of dilation and a scale factor of 2.
SOLUTION
STEP 1
Draw DEFG. Draw rays from D through vertices E, F, and G.

6. EXAMPLE 2
Draw a dilation
STEP 2
Open the compass to the length of DE . Locate E’ on DE so DE’ = 2(DE). Locate F’ and G’ the same way.

7. EXAMPLE 2
Draw a dilation
STEP 3
Add a second label D’ to point D. Draw the sides of D’E’F’G’.

8. Assignment 1 of 2
#3-13 odd, page 629

10. [ ] [ ] [ ] [ ] EXAMPLE 3 Scalar multiplication Simplify the product:4
[ ]
2 – 1 – 3
SOLUTION 4
[ ]
2 – 1 – 3 =
[ ]
4(3) 4(0) 4(1)
4(2) 4(– 1) 4(– 3)
Multiply each element in the matrix by 4.
[ ] =
8 – 4 –12
Simplify.

12. [ ] [ ] 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

13. 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.

14. 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”.

15. Assignment 2 of 2
#15-25 odd, pages 629 & 630