Dilations with no Grid

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Explore Dilations.

Explore this applet to see how the center of dilation and the scale factor affect the image.

Turn off the images and explore the way the lines change. What do you notice?

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Solving Problems on Dilation.

(A). Drag the point C to the place on the ray whose distance from A is twice the distance from B to A

(B). Drag the point D to the place on the ray whose distance from A is half the distance from B to A.

(C). Segment AB (not provided) measures 3 cm. Point O is the center of dilation. How long is the image of AB after a dilation with . . .

(i). Scale factor 5?

(ii). Scale factor 3.7?

(iv). Scale factor ?

(ii). Scale factor s?

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Solving Problems on Dilation.

(A). Use this app to answer the questions below.

(1). Dilate B using a scale factor of 5 and A  as the center of dilation. Which point is its image?

(2). Using H as the center of dilation, dilate  G so that its image is  E. What scale factor did you use?

(3). Using as the center of dilation, dilate so that its image is G. What scale factor did you use?

(4). To dilate F so that its image is B, what point on the diagram can you use as a center?

(5). Dilate H, using  A as the center and a scale factor of . Which point is its image?

(6). Describe a dilation that uses a labeled point as its center and that would take F to H.

(7). Using B as the center of dilation, dilate  H so that its image is itself. What scale factor did you use?

(B). Follow the directions below to perform the dilations in the applet.

  • Select the Dilate From Point tool .​
  • Click on the object to dilate, and then click the center of dilation.
  • When the dialog box opens, enter the scale factor. Fractions can be written with plain text, ex. 1/2.​
  • Click ok​
  • Use the Ray tool and the Distance tool to verify.

(1) Dilate P using C as the center and a scale factor of 4. 

(2). Dilate P using C as the center and a scale factor of

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Here in the applet below are points A and B. C is the image of B using A as the center of dilation and a scale factor of 2. Plot the points for each dilation described.

(1). C is the image of B using A as the center of dilation and a scale factor of 2.

(2). D is the image of A using B as the center of dilation and a scale factor of 2.

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Solving More Problems on Dilation.

Use the applet below to perform the exercises that follow.

(1). 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.

(2). Here are points A and B. Plot the points for each dilation described. D is the image of A using B as the center of dilation and a scale factor of 2.

(3). Here are points A and B. Plot the points for each dilation described. E is the image of B using A as the center of dilation and a scale factor of 1/2.

(4). Here are points A and B. Plot the points for each dilation described. F is the image of A using B as the center of dilation and a scale factor of 1/2.

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Segment AB  measures 3 cm. Point O  is the center of dilation. How long is the image of  AB  after a dilation with . . .

(1). Scale factor of 5?

(2). Scale factor 3.7?

(3). Scale factor of ?

(4). Scale factor ?

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Here is line segment DE and its image D’E’ under a dilation. Use a ruler to find and draw the center of dilation. Label it F.

What is the scale factor of the dilation?