Lesson 3
Dilations with no Grid
Problem 1
Segment \(AB\) measures 3 cm. Point \(O\) is the center of dilation. How long is the image of \(AB\) after a dilation with . . .
- Scale factor 5?
- Scale factor 3.7?
- Scale factor \(\frac 1 5\)?
- Scale factor \(s\)?
Solution
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Problem 2
Here are points \(A\) and \(B\). Plot the points for each dilation described.
- \(C\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of 2.
- \(D\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of 2.
- \(E\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of \(\frac 1 2\).
- \(F\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of \(\frac 1 2\).
Solution
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Problem 3
Make a perspective drawing. Include in your work the center of dilation, the shape you dilate, and the scale factor you use.
Solution
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Problem 4
Triangle \(ABC\) is a scaled copy of triangle \(DEF\). Side \(AB\) measures 12 cm and is the longest side of \(ABC\). Side \(DE\) measures 8 cm and is the longest side of \(DEF\).
- Triangle \(ABC\) is a scaled copy of triangle \(DEF\) with what scale factor?
- Triangle \(DEF\) is a scaled copy of triangle \(ABC\) with what scale factor?
Solution
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(From Unit 2, Lesson 1.)Problem 5
The diagram shows two intersecting lines.
Find the missing angle measures.
Solution
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(From Unit 1, Lesson 14.)Problem 6
- Show that the two triangles are congruent.
- Find the side lengths of \(DEF\) and the angle measures of \(ABC\).
Solution
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(From Unit 1, Lesson 12.)