Lesson 9
Dilations
Let’s dilate figures.
Problem 1
Here is triangle \(ABC\).

- Dilate each vertex of triangle \(ABC\) using \(P\) as the center of dilation and a scale factor of 2. Draw the triangle connecting the three new points.
- Dilate each vertex of triangle \(ABC\) using \(P\) as the center of dilation and a scale factor of \(\frac 1 2\). Draw the triangle connecting the three new points.
-
Measure the longest side of each of the three triangles. What do you notice?
-
Measure the angles of each triangle. What do you notice?
Problem 2
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 \(s\)?
Problem 3
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 \(\frac 1 2\).
Problem 4
Make a perspective drawing. Include in your work the center of dilation, the shape you dilate, and the scale factor you use.