1. Lesson 9-5
Dilations

2. 5-Minute Check on Lesson 9-5
Transparency 9-6
5-Minute Check on Lesson 9-5
Determine whether each regular polygon tessellates the plane. Explain
quadrilateral
octagon
gon
Determine whether a semi-regular tessellation can be created from each figure. Assume each figure has a side length of 1 unit.
4. triangle and square pentagon and square
Which regular polygon will not tessellate the plane?
Yes, Square’s interior angle =  90 = 4
No, Octagon’s interior angle =  135 ≠ integer
No, 15-gon’s interior angle =  156 ≠ integer
Yes, 360 + 290 = 360
No, 108n + 90m ≠ 360
Standardized Test Practice: A
triangle B
quadrilateral C C
pentagon D
hexagon
Click the mouse button or press the Space Bar to display the answers.

3. Objectives
Determine whether a dilation is an enlargement, a reduction, or a congruence transformation enlargement – gotten larger |r| > 1 reduction – gotten smaller |r| < 1 congruence transformation – stayed the same |r| = 1 where r is the scaling factor (similar triangles)

4. Vocabulary
Dilation – a transformation that may change the size of a figure

5. Dilations y x
Five hexagons that are each 50% reduction (1/2) of the size of the one before it
Scale factor is ½, and the center point is the origin (center of the figures)

6. Dilations y x A B A’ B’ CP A* B*
Small dashed lines are the rays along which the dilations occur and the center point is CP . AB = 16, A’B’ = 8 so r = ½ (a reduction |r|<1) A*B* = 8 but since its on the opposite side of CP, r = - ½ (negative = opposite, but still a reduction)

7. Dilations |r| > 1 Enlargement 1 < r |r| < 1 Reduction Ay x
|r| > 1 Enlargement
|r| < 1 Reduction
|r| = 1
Congruence Transformation
1 < r A B
0 < r < 1 C
CP – Center Point CP
These are the lines that the figure’s vertices “travel” on as the figure is
dilated C’
-1 < r < 0
A’B’C’ is with r = -1. B’ A’
-1 > r

8. b. Find the measure of the dilation image or the preimage
a. Find the measure of the dilation image or the preimage of using the given scale factor of CD = 15, r = 3.
Dilation Theorem
Multiply.
Answer: 45
b. Find the measure of the dilation image or the preimage
of using the given scale factor C’D’ = 7, r = - ⅔.
Dilation Theorem
Multiply each side by
Answer: 10.5
Example 5-1a

9. Find the measure of the dilation image or the preimage of
Find the measure of the dilation image or the preimage of using the given scale factor. a. b.
Answer: 32
Answer: 36
Example 5-1b

10. Draw the dilation image of trapezoid PQRS with center C and r = - 3
Since |r| > 1 the dilation is an enlargement of trapezoid PQRS. R' S' P' Q'
Draw Since r is negative, P', Q', R', and S' will lie on respectively.
Locate P', Q', R', and S' so that
Example 5-2a

11. Draw the dilation image of trapezoid PQRS with center C and
Since the dilation is an enlargement of trapezoid PQRS. R' S' P' Q'
Answer: Draw trapezoid P'Q'R'S'.
Example 5-2a

12. Answer: A'(–2, 2), B'(4, –4), C' (–2, –4)
COORDINATE GEOMETRY Triangle ABC has vertices A(–1, 1), B(2, –2), and C(–1, –2). Find the image of ABC after a dilation centered at the origin with a scale factor of 2. Sketch the preimage and the image.
Answer: A'(–2, 2), B'(4, –4), C' (–2, –4)
Example 5-3b

13. image length preimage length
Determine the scale factor used for the dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.
image length preimage length
Simplify.
Since the image is on the opposite side of C from the preimage, the scale factor is negative. So the scale factor is –1. The absolute value of the scale factor equals 1, so the dilation is a congruence transformation.
Answer: –1; congruence transformation
Example 5-4a

14. Determine the scale factor used for each dilation with center C
Determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.
a b.
Answer: reduction
Answer: 2; enlargement
Example 5-4b

15. MULTIPLE-CHOICE TEST ITEM Sharetta built a frame for a photograph that is 20 centimeters by 25 centimeters. The frame measures 400 millimeters by 500 millimeters. Which scale factor did she use?
A 2 B 3 C D
Read the Test Item
The photograph’s dimensions are given in centimeters, and the frame’s dimensions are in millimeters. You need to convert from millimeters to centimeters in the problem.
Example 5-5a

16. Step 1 Convert from millimeters to centimeters.
Solve the Test Item
Step 1 Convert from millimeters to centimeters.
or 40 centimeters
or 20 centimeters
Step 2 Find the scale factor.
frame length photo length
Simplify.
Step 3 Sharetta used a scale factor of 2 to build the frame. Choice A is the correct answer.
Answer: A
Example 5-5a

17. factor of What size poster board will he need to
MULTIPLE-CHOICE TEST ITEM 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.
Answer: B
Example 5-5b

18. Summary & Homework Summary: Homework: Dilations can be
enlargements, (|scaling factor| > 1)
reductions, or (|scaling factor| < 1
congruence transformations (|scaling factor|=1)
Homework:
pg ; 14, 15, 20-23, 30-35