Lesson 3

Dilations with no Grid

Let’s dilate figures not on grids.

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 . . .

  1. Scale factor 5?
  2. Scale factor 3.7?
  3. Scale factor \(\frac 1 5\)?
  4. Scale factor \(s\)?

Problem 2

Here are points \(A\) and \(B\). Plot the points for each dilation described.

Points A and B
  1. \(C\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of 2.
  2. \(D\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of 2.
  3. \(E\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of \(\frac 1 2\).
  4. \(F\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of \(\frac 1 2\).

Problem 3

Make a perspective drawing. Include in your work the center of dilation, the shape you dilate, and the scale factor you use.

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 \(DEF\).

  1. Triangle \(ABC\) is a scaled copy of triangle \(DEF\) with what scale factor?
  2. Triangle \(DEF\) is a scaled copy of triangle \(ABC\) with what scale factor?
(From Unit 2, Lesson 1.)

Problem 5

The diagram shows two intersecting lines.

Find the missing angle measures.

Two intersecting lines, forming an X. 
(From Unit 1, Lesson 14.)

Problem 6

  1. Show that the two triangles are congruent.
  2. Find the side lengths of \(DEF\) and the angle measures of \(ABC\).
Two triangles in an x y plane.
(From Unit 1, Lesson 12.)