Dilations
By David Kwan
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Last updated almost 6 years ago
12 Questions
Note from the author:
This Formative is by: Brian Gervase
This mini lesson introduces students to the physical construction of a dilation. The lesson includes Geogebra applets to PLAY with including guided questions. There are also follow up questions where students practice their skills.
Just Play!
Play in the box below and get a physical feel for what a 'dilation' is in geometry.
Below is a more formal version of a dilation. Let's take a closer look at exactly what is going on here!
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1.
The 'center of dilation' has an effect on the size of the image.
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2.
What should we set k equal to if we want the image to be the exact same as the preimage?
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3.
A dilation will result in an object congruent to the original.
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4.
A dilation will rotate the image relative to the preimage.
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5.
Set k = 3 in the sketch above. Measure OA and AA'. What is the ratio of AA'/OA? Give your answer in the form m/n where m and n are integers. Use a calculator to make your computation if needed.
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6.
Set k = 4 in the sketch above. Measure OA and AA'. What is the ratio of AA'/OA? Give your answer in the form m/n.
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7.
At what value of k will OA' = A'A ?
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8.
What happens when the scale factor in a dilation is negative? As an example, what does is it mean to have a dilation factor of -3 ?
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9.
Use a graphboard to model and answer the question.
Start with the point A(2, 3) and dilate the point by a factor of 4 about the origin (0,0).
What are the coordinates of A' which is the image under this dilation?
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10.
Use a graphboard to model and answer the question.
Start with the point A(2, 3) and dilate the point by a factor of 4 about the point (-1, 5).
What are the coordinates of A' which is the image under this dilation?
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11.
Consider the dilation from the problem above. What is the vector transformation that is equivalent to the dilation? That is, what is the vector AA'? Write your answer in the form <k,m> .
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12.
Write a reflection statement on this lesson. Be sure to define what a 'dilation' is in your own words. A good statement should make the connection between the size of the image and the ratio of the distances to the center of dilation.