# 11.03.15 Dilations ```Name ______________________________________________
Classwork: Dilations AMT12 Day1
Date____________________
Ms. Wong, Geometry
Warm Up:
1. Solve for the unknown in the following proportions.
3
1
a. 𝑎 = 8
4
2
b. 𝑏+2 = 7
4
𝑥
c. 5 = 𝑥+8
2. For the filming of a recent sci-fi movie, a model spaceship made to a scale of 1:16 was used.
In the movie, the ship is supposed to be 104 feet long. Set up a proportion and solve it to find the
length of the model.
3. Write a definition for dilation.
4. How can you use the surveyor’s measurements to find the distance across the lake?
(AMT12 > Overview > Panel 4 > Slides 2, 3, and 4)
A recap…
1. What is an isometry?
2. How is a dilation different from an isometry?
In this topic, we will examine DILATIONS—a non-rigid transformation, which we have briefly
discussed in topics 2 and 3, but did not expand upon. Dilations are a shrink or stretch of an
original figure (pre-image). Pre-images are labeled by their vertices (all capital letters) and their
images are labeled by the same capital letters, but with apostrophes that we call “prime”.
**NOTE: The scale factor is always multiplied to the measurements of the pre-image. OR, in
coordinate geometry, simply multiply the coordinates (x, y) by the scale factor to obtain the
coordinates of the image.
The rule of a dilation is 𝑘(𝑥, 𝑦) = (𝑘𝑥, 𝑘𝑦) where k is the scale factor.
Dilate triangle ABC by a scale factor of 3 where the center of dilation is at point O. You will
need a straight edge and a compass, or some other measuring tool.
In the figure below, O is the center of dilation and the scale factor is 3.
3.
**Note: The scale factor is always computed as the ratio of the image over the pre-image.
4. How do the ratios you computed above compare to the scale factor?
Use the diagram above to answer questions 5-7
5. As the scale factor changes, what do you notice about the measures of the corresponding
angles? [EX1, p4]
6. What do you notice about the ratios of the lengths of the corresponding sides? [EX1, p4]
7. How is the ratio of the lengths of the corresponding sides related to the scale factor when the
scale factor is positive? [EX1, p4]
8. When the scale factor approaches zero, at what point does the image triangle, ∆𝑅′𝑆′𝑇′ become
a reduction of ∆𝑅𝑆𝑇 instead of an enlargement? [EX1, p4]
9. What happens when the scale factor is negative? [EX1, p4]