1. Class Greeting

2. Chapter 7 – Lesson 1
Dilation

3. Objective: The students will be able to apply the concepts involving Dilation.

4. Vocabulary dilation scale factor enlargement reduction
isometry dilation
center of dilation

5. A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar.

6. A scale factor describes how much the figure is enlarged or reduced
A scale factor describes how much the figure is enlarged or reduced. For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by k: (a, b)  (ka, kb).

7. If the scale factor of a dilation is greater than 1 (k > 1), it is an enlargement.
If the scale factor of a dilation is a positive number less than 1 (k < 1), it is a reduction.
Helpful Hint
Helpful Hint
If the scale factor of a dilation is 1 (k = 1), it is an isometry dilation.
It produces an image that coincides with the preimage. The two figures are congruent and on top of each other.

8. A dilation with center O.

9. Example 1: Drawing Dilations
Draw the image of ∆WXYZ under a dilation with a scale factor of 2 and the center of dilation P.
Step 1 Draw a line through P and each vertex.
Step 2 On each line, mark twice the distance from P to the vertex. W’ X’
Step 3 Connect the vertices of the image. Y’ Z’

10. Step 1 Draw a line through Q and each vertex.
Your Turn
Copy the figure and the center of dilation. Draw the dilation of RSTU using center Q and a scale factor of 3.
Step 1 Draw a line through Q and each vertex.
Step 2 On each line, mark twice the distance from Q to the vertex. R’ S’
Step 3 Connect the vertices of the image. T’ U’

11. Example 2: Dilations
On a sketch of a flower, 4 in. represent 1 in. on the actual flower. If the flower in the sketch has a 3 in. diameter, find the diameter of the actual flower.
The scale factor in the dilation is 4.
Let the diameter of the actual flower be d in.
4d = 3
d = 0.75 in.
Answer: the diameter of the actual flower is 0.75 in.

12. Your Turn
A rectangle on a transparency has length 6cm and width 4 cm . On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection.
Answer: the perimeter of the rectangle in the projection is 240 cm.

13. Example 3: Drawing Dilations in the Coordinate Plane
Graph RSTU and its images after a composition of dilations centered at the origin with a scale factor of and a scale factor of 2, given R(0, 0), S(4, 0), T(2, -2), and U(–2, –2).
The first dilation of (x, y) is

14. Graph the preimage and images.
Preimage RSTU: R(0, 0), S(4, 0), T(2, -2), and U(–2, –2)
T’’
U’’ R’ S’ T’ U’ R S T U
R’’
S’’

15. Your Turn
Draw the image of the triangle with vertices
P(–4, 4), Q(–2, –2), and R(4, 0) under a dilation with a scale factor of centered at the origin.
The dilation of (x, y) is

16. Graph the preimage and image.Q’ R’ R Q

17. Example 4: Drawing Dilations in the Coordinate Plane
Draw rays from A through the vertices of RST.
Graph point A and RST R S R’ T S’ T’ A

18. Draw rays from A through the vertices of RST.
Your Turn
Graph RST and its image after a dilation centered at A(20, 14) with a scale factor of 3 given R(14, 13), S(19, 11) and T(14, 10).
Draw rays from A through the vertices of RST.
Graph point A and RST
Multiply the distances from A to the vertices of RST by the scale factor 3 and plot those points.
A shortcut is to multiply the “ups” and “overs” by 3. A R R’ S T S’ T’

19. Kahoot!

20. Lesson Summary:
Objective: The students will be able to apply the concepts involving Dilation.

21. Preview of the Next Lesson:
Objective: The students will solve problems involving Similar Polygons.

22. Stand Up Please