11.03.15 Dilations

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Name ______________________________________________
Classwork: Dilations AMT12 Day1
Date____________________
Ms. Wong, Geometry
Warm Up:
1. Solve for the unknown in the following proportions.
3
1
a. ๐‘Ž = 8
4
2
b. ๐‘+2 = 7
4
๐‘ฅ
c. 5 = ๐‘ฅ+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 surveyorโ€™s measurements to find the distance across the lake?
(AMT12 > Overview > Panel 4 > Slides 2, 3, and 4)
A recapโ€ฆ
1. What is an isometry?
2. How is a dilation different from an isometry?
In this topic, we will examine DILATIONSโ€”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 โ€œprimeโ€.
**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 ๐‘˜(๐‘ฅ, ๐‘ฆ) = (๐‘˜๐‘ฅ, ๐‘˜๐‘ฆ) 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, โˆ†๐‘…โ€ฒ๐‘†โ€ฒ๐‘‡โ€ฒ become
a reduction of โˆ†๐‘…๐‘†๐‘‡ instead of an enlargement? [EX1, p4]
9. What happens when the scale factor is negative? [EX1, p4]
10. Complete the following statements to summarize your findings about dilations.
11. Complete the following statements that describe a dilation with scale factor s. [EX1, p.6]
12. This illustration shows a dilation with a scale factor of -2. What is the ratio Rโ€™J:RJ?
[EX1, p7]
13. Do the relationships you found in question 11 hold true even for if the triangle is distorted?
[EX1, p8]
14. Write the definition for similar polygons. [EX1, p9]
15. Apply the definition of similar polygons to decide whether each pair of polygons is similar or
not similar. Match the pairs of polygon to the appropriate category in the table. [EX1, p10]
16. Suppose the two triangles shown are similar. Find the unknown side length.
17. Suppose the two figures shown are similar. Find the scale factor that made the enlargement.
Homework Assignment: AgileMind Topic 12 โ€œMore Practiceโ€ Questions # 1- 4, 6, 13, 14
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