Explore the applet and observe the dilation of triangle . The dilation always uses center ** P**, but you can change the scale factor.

What connections can you make between the scale factor and the dilated triangle?

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**Exploring More on Dilations.**

**(A). Explore the dilations on the graph below and answer the questions.**

Use the following relation to find the scale factor ** k**.

(4). What do notice?

You can also finding the scale factor, K, using the ordered pairs.

(5). Slide k = 2 in the applet. What are the coordinates of **A**, **B**, **A’** and **B’**?

(6). How can you find the scale factor using the ordered pairs?(6).

**(B).** **Explore the dilations on the graph below and answer the questions.**

(1). How does the scale factor and center influence the location of the pre-image and corresponding image points with regards to the center?

(2). How does the scale factor and center influence the length of the pre-image sides and their corresponding image sides?

(3). How does the scale factor and center influence the location of the image with regards to the pre-image?

(4). What are other relationships between the pre-image, image, scale factor and center?

Using the second graph below,

(6). find the relationship between the scale factor and the ratio of the area of the image to the area of pre-image.

(7). find the relationship between the scale factor and the ratio of the perimeter of the image to the perimeter of pre-image.

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**Exploring More on Dilations.**

**(1). **Triangle EFG was created by dilating triangle ABC using a scale factor of 2 and center D. Triangle HIJ was created by dilating triangle ABC using a scale factor of and center D.

What would the image of triangle ABC look like under a dilation with scale factor 0?

**(2)**. What would the image of the triangle look like under dilation with a scale factor of -1? If possible, draw it and label the vertices A’, B’ and C’. If it’s not possible, explain why not.

If it’s not possible, explain why not.

If possible, describe what happens to a shape if it is dilated with a negative scale factor. If dilating with a negative scale factor is not possible, explain why not.

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**Exploring More on Dilations.**

Use the applet below to explore the properties of dilating a polygon from different points on the coordinate plane.

Note that ScaleE is the scale factor for dilating from point E, ScaleA is the scale factor for dilating from point A, and so on.

**(1).** If you dilate from point E, what happens when you increase the scale factor for dilation (ScaleE)? What happens when you decrease the scale factor for dilation?

**(2). **If you dilate from point A, what happens when you increase the scale factor for dilation (ScaleA)? What happens when you decrease the scale factor for dilation?

**(3).** If you dilate from point F, what happens when you increase the scale factor for dilation (ScaleF)?

**(4).** If you dilate from point H, what happens when you increase the scale factor for dilation (ScaleH)?

**(5). **Following the pattern observed above, how could you find the coordinates of the vertices of the polygon if you dilated from point G?

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Quadrilateral ABCD is dilated with center , taking B to B’. Draw A’B’C’D’.

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Triangle B and C have been built by dilating Triangle A. Find the center of dilation.

(1). Triangle **B** is a dilation of **A **with approximately what scale factor?

(2). Triangle **A** is a dilation of **B **with approximately what scale factor?

(3). Triangle **B** is a dilation of **C **with approximately what scale factor?

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Here below is a triangle. Draw the dilation of ABC, with center , and scale factor of 2. Label this triangle A’B’C’.

On the graph above, draw the dilation of triangle , with center , and scale factor of . Label this triangle . Is a dilation of triangle ? If yes, what are the center of dilation and the scale factor?

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