1. Dilations Dilations Dilations Dilations Dilations Dilations Dilations
Section 9.5
Dilations
Dilations
Dilations
Dilations
Dilations

2. Determine the scale factor for a given dilation.
Determine whether a dilation is an enlargement, a reduction, or a congruence transformation.
Determine the scale factor for a given dilation.
dilation
similarity transformation
Standard Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
Lesson 5 MI/Vocab

3. Dilation Center: C Scale Factor: r or k (the book uses both)
Def: A transformation that maps every point P to a point P’ so that the following properties are true:
P’ lies on
The scale factor is:

4. Scale Factor If r > 1, the dilation is called an enlargement.
If r < 1, the dilation is called a reduction.
If r = 1, the dilation is called a congruence transformation.
(Just like in chapter 7) A scale factor can also be found by comparing corresponding lengths in a ratio.

5. Example #1 r < 1 reduction
Determine the scale factor, then state if the dilation is an enlargement, reduction or congruence transformation.
r < 1 reduction

6. Example #2 r > 1 enlargement
Determine the scale factor, then state if the dilation is an enlargement, reduction or congruence transformation.
r > 1 enlargement

7. Theorem 9.2:
If a dilation with center C and a scale factor of r transforms A to A’ and B to B’, then:
A’B’ = |r|(AB)
Algebraic hint: AB =
Lesson 5 KC1

8. Example #3
Given PQ = 1, Q’R’ = 4, use the scale factor to find P’Q’ and QR. 1

9. Example #3
Given PQ = 1, Q’R’ = 4, use the scale factor to find P’Q’ and QR. 4

10. Determine Measures Under Dilations
A. Find the measure of the dilation image C′D′ using the given scale factor for
CD = 15, r = 3.
Answer: 45
Lesson 5 Ex1

11. B. Find the measure of the preimage using the given scale factor if
Determine Measures Under Dilations
B. Find the measure of the preimage using the given scale factor if
Multiply each side by
Answer: 10.5
Lesson 5 Ex1

12. A. Find the measure of the dilation image A′B′ using the given scale factor for AB = 16, r = –2.
Lesson 5 CYP1

13. B. Find the measure of the preimage using the given scale factor for A′B′ = 24, r = .
Lesson 5 CYP1

14. Which diagram shows the dilation image of ΔLMN with center C and ?
A B.
C D. A B C D
Lesson 5 CYP2

15. Multiply the coordinates by the scale factor.
Theorem 9.3
If is the preimage of a dilation centered at the origin with a scale factor k, then the image is
Multiply the coordinates by the scale factor.
Lesson 5 TH2

16. COORDINATE GEOMETRY Trapezoid EFGH has vertices E(–8, 4), F(–4, 8),
Dilations in the Coordinate Plane
COORDINATE GEOMETRY Trapezoid EFGH has vertices E(–8, 4), F(–4, 8),
G(8, 4) and H(–4, –8). Find the image of trapezoid EFGH after a dilation centered at the origin with a scale factor of Sketch the preimage and the image.
Lesson 5 Ex3

17. Hint: If you did it right… Answer: E'(–2, 1), F'(–1, 2), G'(2, 1),
Dilations in the Coordinate Plane
Answer:
E'(–2, 1),
F'(–1, 2),
G'(2, 1),
H'(–1, –2)
Hint:
If you did it right…
Lesson 5 Ex3

18. COORDINATE GEOMETRY Triangle ABC has vertices A(–1, 1), B(2, –2), and C(–1, –2). Find the image of ΔABC after a dilation centered at the origin with a scale factor of 2. Sketch the preimage and the image.
A. B. C.
D. none of the above A B C D
Lesson 5 CYP3

19. frame length photo length
Scale Drawing
Sharetta built a frame for a photograph that is 20 centimeters by 25 centimeters. The frame measures 40 centimeters by 50 centimeters. Which scale factor did she use?
Find the scale factor.
frame length photo length
Simplify.
Answer: Sharetta used a scale factor of 2 to build the frame.
Lesson 5 Ex5

20. Ruben is making a scale drawing of the front of his house
Ruben is making a scale drawing of the front of his house. His house is 48 feet wide and 30 feet high at its highest point. Ruben decides on a dilation reduction factor of What size poster board will he need to make a complete drawing?
A. 19 in. by 26 in.
B. 22 in. by 30 in.
C in. by 28 in.
D. 16 in. by 29 in. A B C D
Lesson 5 CYP5

21. Homework:
Pg 529:
#1, 2, 6 – 8, 10 – 19 all,
26 – 32 even.

22. Identify Scale Factor
A. Determine the scale factor used for the dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation. 6 2
Lesson 5 Ex4

23. D. 1; congruence transformation
A. For the green preimage, determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.
A. 2; enlargement B. C.
D. 1; congruence transformation A B C D
Lesson 5 CYP4

24. B. For the green preimage, determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.
A. 2; enlargement B. C.
D. 3; enlargement A B C D
Lesson 5 CYP4