Bellwork Find the geometric mean of 5 & 18 Find the geometric mean of 3 & 44 Solve for x

Solve for x, if AB & CD are parallel

What point is twice as far from the origin as (3, 5)?

x

x-2

53

A

B

C

D

x2x-1

8

12

No Clickers

Bellwork Solution Find the geometric mean of 5 & 18

5 18 x

3 10x5 2 9 x

Bellwork Solution Find the geometric mean of 3 & 44

3 44 x

2 33x3 4 11 x

Bellwork Solution Solve for x

x

x-2

53 5

2 33 5( 2)

3 5 10

2 10

5

x

xx x

x x

x

x

Bellwork Solution Solve for x, if AB & CD are parallel

A

B

C

D

x 2x-1

812

8

2 1 1212 8(2 1)

12 16 8

4 8

2

x

xx x

x x

x

x

Bellwork Solution What point is twice as far from the origin as (3, 5)?

(3,5)

(2 3,2 5)

(6,10)

2 21

2 2

(5 0) (3 0)

5 3

25 9

34

d

2 2

2

2 2

(10 0) (6 0)

10 6

100 36

136 4 34 2 34

d

Perform Similiarity Transformations

Section 6.7

Test on Wednesday

The Concept We’ve covered most of chapter 6, but we have yet to apply our

understanding of similarity to objects on the coordinate plane. Today we’re going to use our understanding of similarity and

transformations to discuss similarity transformations.

Review We’ve seen three kinds of transformations thus far

Translations Shifts or moves up or down and right or left

Rotations Object rotations a direction and angle about the origin

Reflections Flips of an object either over the x-axis or the y-axis

The last one that we will learn about is dilations

Definitions Dilation

Special kind of transformation that stretches or shrinks a figure to create a similar figure

Figures are either reduced or enlarged Type of similarity transformation

Y

X

Y

X

Definitions Center of Dilation

Fixed point with which the object is dilated Scale factor of dilation

Ratio of a side length of the image to the corresponding side length of the original figure

Y

X

Y

X

Coordinate Notation We prefer to be able to notate for dilations For dilations centered at the origin

(x,y)(kx,ky), where k is a scale factor If 0<k<1, reduction If k>1, enlargement

Drawing a Dilation Draw a dilation of an object with vertices (0,2), (5, 3) & (5,-3)

using a scale factor of 2

(0,2)

(5,3)

(5, 3)

Y

X

Y

X

(0,4)

(10,6)

(10, 6)

Drawing a Dilation Draw a dilation of an object with vertices (4,6), (2, 4) & (6,-6)

using a scale factor of 1/2

(4,6)

(2,4)

(6, 6)

Y

X

Y

X

(2,3)

(1,2)

(3, 3)

ExampleDraw a dilation of a quadrilateral ABCD with vertices A(2,2),

B(4,2), C(4,0), D(0,-2). Use a scale factor of 1.5 and label the object FGHJ Y

X

Y

X

Scale or k factor We’ve discussed scale factor before and defined it as

The quotient of a side length of the second object and the corresponding side length of the first object

This property of dilations is no different For example, find the scale factor of these two objects

Y

X

Y

X1

2 63

2

Example We can also determine k factor from points Find the k factor between these two objectsY

X

Y

X

What do we needin order to give

an accurate answer

Example Is the green object a dilation of the yellow one?

Y

X

Y

X

How do we know?

( 1,3) ( 2,6) (4, 4) (8,8)(3,1) (6,2)(0,0) (0,0)

Practical Example You are using a photo quality printer to enlarge a digital picture.

The picture on the computer screen is 6 centimeters by 6 centimeters. The printed image is 15 cm by 15 cm. What is the scale factor of the enlargement?

15

6

5

2

Homework

6.7 Exercises 1, 2-8 even, 9-23, 25, 26

ExampleDraw a dilation of a quadrilateral ABCD with vertices A(-3,5),

B(3,4), C(4,-2), D(-3,-2). Use a scale factor of 1.5 and label the object FGHJ Y

X

Y

X

Most Important Points Definition of Dilation Bounds for the k scalar Performing Dilations Finding k factor from points