Dilations and Similarity Points

Unit 2 Recap

by Lesley Brantley

​Dilations

​What are they?

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​What makes a dilation bigger/smaller?

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​Scale Factor is 2. What are the coordinates of the image?

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​A (3,2)

​B (-3, -4)

​C (0, 3)

​Scale Factor is 1/2. What are the coordinates of the image?

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​A ( 6, 4)

​B (-4, 2)

​C (0. -2)

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Multiple Choice

Choose the correct scale factor:

• 2
• 3
• 1/3
• 1/2

Multiple Choice

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

• (5,3), (6,2), (1,-2)
• (6,0), (9,-3), (-6,-15)
• (2/3,0), (1,-1/3), (-2/3,-5/3)
• (-1,-3), (0,-4), (-5,-8)

Multiple Choice

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)
• (20,12)
• (-20,-12)
• (-5,-3)

Multiple Choice

What is the scale factor from ABCD to MNOP?

• 2/3

• 3/2

• 2

• 3

​Similarity-- occurs as a result of a dilation

​Shapes are similar if...

​1. The angles are CONGRUENT

​2. The side lengths are PROPORTIONAL!!!

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​Remember-- triangles have 180 degrees.

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​These triangles are similar because their angles measures are CONGRUENT!!!

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

The measures of the angles in a triangle are 53⁰,78⁰, and 49⁰.  A similar triangle is created by using a dilation with a scale factor of 2.  What are the measures of the angles of this triangle?

• 53⁰,78⁰, and 49⁰
• There is not enough information to answer this question.
• 106⁰,156⁰, and 98⁰
• 26.5⁰,39⁰, and 24.5⁰

​Finding missing sides of similar shapes

​1. Look to see if you can easily identify the scale factor.

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​OR

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​2. set up the ratios and cross multiply to solve.

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Multiple Choice

Solve for X.

• 2 ft
• 3 ft
• 4 ft
• 6 ft

Multiple Choice

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75
• 9.75
• 10
• 12

Multiple Choice

What is the value of X?

• X=4
• X=6
• X=3
• X=2

​Slope

​How do we find slope?

​Slope

​vertical

​horizontal

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Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2
• -2

Multiple Choice

Find the slope of the line.

• 1/4
• -1/4
• -4
• 4