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/x2 - 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