Dilations
Similarity & Proportions
Slope
100

A dilation is a type of transformation that does what to a figure?

Stretches or shrinks

100

Similar figures have the same shape, same angles, but they have different/proportional ____________

Similar figures have proportional size

100

Slope describes how ______________ a line is.

Steep

200

What operation (+ - x ÷) do you use to dilate? 

Multiplication

Dilating a shape = k · side length

Dilating on a grid = (k·x, k·y)

200

Find the missing side of the triangle.


Set up a proportion!

15/10 = 30/x

Then cross multiply

300 = 15x

x = 12

200

What is the difference between 0 slope and undefined slope? (Describe the lines)

0 slope is a horizontal line

undefined slope is a vertical line

300

What does scale factor tell you?

How much a figure shrinks or stretches

300

You have an old figure and a new one. 

How do you find the scale factor? 


Scale factor: k = new ÷ old

300

Find the slope of each line.


Slope = rise/run

1) 4/2 or 2

2) -5/4

3)7/5

400

This triangle is dilated with a scale factor of k=3

What are its new side lengths?


5 x 3 = 15

4 x 3 = 12

3 x 3 = 9 

400

Find the scale factor for these similar triangles.


k = new ÷ old

You only need to use one side!

8 ÷ 4 = 2

10 ÷ 5 = 2

6 ÷ 3 = 2

400

Find the slope of 2 points: (-3, 4) and (5, -3)

Slope of 2 points = y2 - y1/x- x1

-3 - 4 / 5-(-3)

-7/8 

500

Triangle ABC is dilated with a scale factor of k=0.5 

Find the new points.

A (2, 4) 

B (3, 6)

C (-2, 4)

A (2 ⋅ 0.5, 4 ⋅ 0.5) = A' (1, 2)

B (3 ⋅ 0.5, 6 ⋅ 0.5) = B' (1.5, 3)

C (-2 ⋅ 0.5, 4 ⋅ 0.5) = C' (-1, 2)

500

Find the scale factor using the x value of point A and A'.


A: (4, 6)

A': (2, 3)

k = 2 ÷ 4

k = 0.5

500

Write an equation for the line (y=mx+b) using the graph. 


y = (1/2)x -2

m: slope (rise/run) = 1/2

b: y-intercept = -2



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