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Unit 6 Dilations Exploration

Autore:Katie King, Shannon Rush
Argomento:Dilatazione

Directions: Complete the questions below and fill out your notes on Day 3 using the information below.

A dilation is a transformation in which a figure is enlarged or reduced with respect to a given point. The point is called the "center of dilation." Directions on how to use the applet below: Click the Dilate button below to show the dilation of the triangle with respect to the point. Use the slider to change the scale factor. Move the points of the original triangle. Essentially play with all the factors involved! As you do, pay attention to the effects on the points, segments, and angles.

Problem 1. Use the Geogebra applet above to answer the following questions...

In one sentence, describe how the triangle changes from the pre-image to image when d>1?

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Problem 2. Use the Geogebra applet above to answer the following questions...

In one sentence, describe how the triangle changes from the pre-image to image when d<1?

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Problem 3. Use the Geogebra applet above to answer the following questions...

What DOES NOT change as you change the d value?

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Problem 4.

In Unit 1, we learned about isometries. Isometries are transformations that create congruents preimages and images. Based on the applet above, do you think a dilation is an isometry? Write one sentence to explain why you think a dilation is or is not an isometry.

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NOTES: Fill in your notes on page 14 using the information below

In Unit 1, we learned about different types of transformations. We focused on isometries, or transformations that created congruent figures. There are other types of transformations also. One of these is called dilations. This is a transformation that can cause a figure to reduce or enlarge in size. Dilations create similar figures (Same shape, DIFFERENT size). A dilation is NOT an isometry. (Except in a special case) The description of a dilation includes the scale factor and the center of dilation. When dilating a figure, we use the center of dilation as a reference point to scale the figure. It's the point from which the figure is enlarged or reduced. The scale factor indicates how much larger or smaller the figure becomes. If the scale factor, k, is greater than 1, the dilation is called an enlargement. If the scale factor, k, is between 0 and 1, the dilation is called a reduction.

Problem 5. Use the Geogebra applet above to answer this question...

Move the preimage to wherever you want. How far away is point A from point D? And, how far away is point A' from point D?

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Problem 6.

In Unit 1, we described translations using an algebraic rule. For instance, moving a point left 2 units and up 1 unit would be written as the rule . Move the center of dilation, Point D, to the coordinate (0,0). Change the scale factor, d, to 3. Select the algebraic rule that describes a dilation by a factor of 3.

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NOTES: On page 14...

Using the geogebra applet, complete problems 1-3 on page 14 of your notes. Ask you group mates a question if you get stuck! Questions like... "How do I find the scale factor?" "What did you do to find the algebraic rule?" "How do you know if that algebraic rule is correct?" "What did you do to find the scale factor?"

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