1. Five-Minute Check (over Lesson 6) Mathematical Practices Then/Now
Key Concept: Dilation
Example 1: Draw a Dilation
Example 2: Real-World Example: Find the Scale of a Dilation
Key Concept: Dilations in the Coordinate Plane
Example 3: Dilations in the Coordinate Plane
Lesson Menu

2. Complete the statement about parallelogram LMNO.?
Complete the statement about parallelogram LMNO. A. B. C. D.
5-Minute Check 1

3. Complete the statement about parallelogram LMNO.? A. B. C. D.
5-Minute Check 2

4. Complete the statement about parallelogram LMNO.  OLM  ____?
A.  MNO
B.  LON
C.  MPN
D.  MPL
5-Minute Check 3

5. Complete the statement about parallelogram LMNO.? A. B. C. D.
5-Minute Check 4

6. Find the measure of each interior angle.
m A = 60, m B = 120, m C = 60, m D = 120
B. m A = 65, m B = 115, m C = 65, m D = 115
C. m A = 65, m B = 115, m C = 60, m D = 120
D. m A = 70, m B = 110, m C = 70, m D = 110
5-Minute Check 5

7. Which of the statements about an isosceles trapezoid is false?
A. The diagonals are congruent.
B. Two sides are both congruent and parallel.
C. Two pairs of base angles are congruent.
D. One pair of sides are congruent.
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
5 Use appropriate tools strategically.
Content Standards
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. MP

9. Draw dilations in the coordinate plane.
You identified dilations and verified them as similarity transformations.
Draw dilations.
Draw dilations in the coordinate plane.
Then/Now

10. Concept

11. Since k > 1, the dilation is an enlargement of trapezoid PQRS.
Draw a Dilation
Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3.
Since k > 1, the dilation is an enlargement of trapezoid PQRS.
Example 1

12. Draw a Dilation
Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3.
Locate P', Q', R', and S' so that
Example 1

13. Answer: Draw trapezoid P'Q'R'S'.
Draw a Dilation
Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3.
Answer: Draw trapezoid P'Q'R'S'.
Example 1

14. Which diagram shows the dilation image of ΔLMN with center C and ?
A. B.
C. D.
Example 1

15. Find the Scale Factor of a Dilation
PUPPETS To create the illusion of a “life-sized” image, puppeteers sometimes use a light source to show an enlarged image of a puppet projected on a screen or wall. Suppose that the distance between a light source L and the puppet is 24 inches (LP). To what distance PP' should you place the puppet from the screen to create a inch tall shadow (I'M') from a 9-inch puppet?
Example 2

16. Find the Scale Factor of a Dilation
Understand This problem involves a dilation. The center of the dilation is L, LP = 24 in., IM = 9 in., I'M' = 49.5 in. You are asked to find PP'.
Plan Find the scale factor of the dilation from the preimage IM to the image I'M'. Use the scale factor to find LP and then use LP and LP' to find PP'.
Example 2

17. Find the Scale Factor of a Dilation
Solve The scale factor k of the enlargement is the ratio of the length on the image to a corresponding length on the preimage.
Scale factor of image
image = I'M', preimage = IM
Divide.
Example 2

18. Use this scale factor of 5.5 to find LP'.
Find the Scale Factor of a Dilation
Use this scale factor of 5.5 to find LP'.
LP' = k(LP) Definition of dilation
= 5.5(24) k = 5.5 and LP = 24
= 132 Multiply.
Use LP' and LP to find PP'.
LP + PP' = LP' Segment Addition
24 + PP' = 132 LP = 24 and LP' = 132
PP' = 108 Subtract 24 from each side.
Example 2

19. Find the Scale Factor of a Dilation
Answer: So, the puppet should be placed so that the distance from it to the screen (PP') is 108 inches.
Check Since the dilation is an enlargement, the scale factor should be greater than 1. Since 5.5 > 1, the scale factor is reasonable.
Example 2

20. PUPPETS Suppose you have a similar situation with the puppet and light source. The distance between the light source L and the puppet is 30 inches (LP). To what distance should you place the puppet from the screen to create a 54-inch tall shadow (I'M') from a 6-inch puppet?
A. 100 inches
B. 180 inches
C. 220 inches
D. 240 inches
Example 2

21. Concept

22. Multiply the x- and y-coordinates of each vertex by the scale factor,
Dilations in the Coordinate Plane
Graph the image of each polygon with the given vertices after a dilation at the indicated center with the given scale factor.
A. E (−8, 4), F (−4, 8), G (8, 4), and H (−4, −8); origin; k =
Multiply the x- and y-coordinates of each vertex by the scale factor,
Example 3

23. Graph the preimage and image.
Dilations in the Coordinate Plane
Graph the preimage and image.
Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), H'(–1, –2)
Example 3

24. Dilations in the Coordinate Plane
Graph the image of each polygon with the given vertices after a dilation at the indicated center with the given scale factor.
B. A(−2, −4), B(3, 2), C(0, 4); (1, 2); 1.5
Multiply the x- and y-coordinates of each vertex by the scale factor, 1.5.
Preimage (x, y)
Image (1.5x, 1.5y)
A(–2, –4)
a(–3, –6)
B(3, 2)
b(4.5, 3)
C(0, 4)
c(0, 6)
Example 3

25. Dilations in the Coordinate Plane
Answer:
Example 3

26. Triangle ABC has vertices A(–1, 1), B(2, –2), and C(–1, –2)
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
Example 3