Transcript 7.5 and 7.6: Dilation

Happy Tuesday!
Take Out: Homework #5
HW #6 : p 491 #10, 11; p 498 #1-5, 8, 17, 18
Updates: Unit 4 Part 1 Test ( 7.1-7.6 )
Tuesday/ Wednesday
Agenda
Review HW
Finish 7.5- Investigation
7.6: Exploration
7.6: Dilations
Test Master
7.5: Using Proportional
Relationships
You will be able to:
(1) Use ratios to find area and perimeter of similar figures.
Whiteboards
1Maria is 4 ft 2 in. tall. To find the
height of a flagpole, she
measured her shadow and the
pole’s shadow. What is the
height h of the flagpole?
2. A blueprint for Latisha’s
bedroom uses a scale of 1 in.:4
ft. Her bedroom on the
blueprint is 3 in. long. How
long is the actual room?
7-5 Using Proportional Relationships
We have discussed a lot about similar triangles and their side
lengths.
What about similar triangles and their perimeters?
What about similar triangles and their areas?
7-5 Using Proportional Relationships
Whiteboard
o Take 2 minutes to write down your definition of perimeter and
your definition of area.
o Lets investigate what the relationship might be between the
similarity ratio, perimeter, and area of a figure.
7-5 Using Proportional Relationships
You will have the next 8 minutes to complete the Investigation
on the back of your notes.
7-5 Using Proportional Relationships
7-5 Using Proportional Relationships
Example 3
Given that ∆LMN ~ ∆QRT, find the perimeter P and area A of ∆QRS.
Whiteboards
∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A =
96 mm2 for ∆DEF, find the perimeter and area of ∆ABC.
7.6: Dilations and Similarity in
the Coordinate Plane
You will be able to:
(1) Dilate figures in the coordinate plane.
Whiteboards
Write/ draw everything that you know about dilations
Exploration
For step 4, one person finds the length of each side for
triangle ABC, another partner does it for A’B’C’, another
for A’’B’’C’’.
Recall: What is the distance formula?
7.6: Dilations and Similarity in
the Coordinate Plane
Dilation
0 Transformation that changes the size of a figure, but not its
shape.
7.6: Dilations and Similarity in
the Coordinate Plane
Scale Factor
0 describes how much the figure is enlarged or reduced.
0 Written in the form: (x, y)  (kx, ky)
0 scale factor greater than 1 (k>1 ) is an enlargement , or
expansion.
0 scale factor greater than 0 but less than 1
( k < 1) is a reduction, or contraction.
7.6: Dilations and Similarity in
the Coordinate Plane
Table-Share:
0 Describe a real life object that is enlarged
0 Describe a real life object that is reduced
Example 1: Computer Graphics Application
Draw the border of the photo after a dilation with scale factor
7.6: Dilations and Similarity in
the Coordinate Plane
Whiteboards!
Given that ∆MON ~ ∆POQ and coordinates P (–15, 0),
M(–10, 0), and Q(0, –30), find the coordinates of N
and the scale factor.
Example 3!
Draw the image of the triangle with vertices R(0, 0),
S(4, 0), T(2, -2), and U(–2, –2) under a dilation
centered at the origin with a scale factor of -½.
Example 3!
Quiz Master
Create your own word problem and solve it that
involves one of the following:
o Indirect Measurement
o Scale Drawing
o Ratio of Area and Perimeter
I may use this on your test!