10-15-24 Introduction to Dilations
10-15-24 Introduction to Dilations Student Handout
1.
Determine the scale factor and the location of your center of dilation from triangle ABC to triangle A'B'C'. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped polygon ABCDE on to polygon A'B'C'D'E'.
2.
Determine the scale factor and the location of your center of dilation from polygon ABCDE to polygon A'B'C'D'E'. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped polygon ABCDE on to polygon A'B'C'D'E'.
3.
Determine the scale factor and the location of your center of dilation from quadrilateral ABCD to quadrilateral A'B'C'D'. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped triangle ABC on to triangle A'B'C'.
4.
Determine the scale factor and the location of your center of dilation from triangle ABC to triangle DEF. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped triangle ABC on to triangle DEF.
Use your discoveries from examples 1-4 to answer the following questions.
How does the center of dilation affect how a shape "dilates"? What happens when the point is away from the shape, in the middle of the shape, or on a vertex?
When the scale factor is greater than one, does the image move closer to the center of dilation or further away?
When the scale factor is less than one, does the image move closer to the center of dilation or further away?
Why were we unable to map triangle ABC on to triangle DEF in question 4?
5.
Using the Line tool 
, connect all pairs of corresponding points. Plot a point where all of the lines intersect; this is your center of dilation.
*Mark your center of dilation on your student handout. Determine the scale factor from ABCD to A'B'C'D' by looking at lengths of corresponding sides and distances and write down that scale factor on your student handout as well.
, connect all pairs of corresponding points. Plot a point where all of the lines intersect; this is your center of dilation.
*Mark your center of dilation on your student handout. Determine the scale factor from ABCD to A'B'C'D' by looking at lengths of corresponding sides and distances and write down that scale factor on your student handout as well. 6.
Using the Line tool , connect all pairs of corresponding points. Plot a point where all of the lines intersect; this is your center of dilation.
*Mark your center of dilation on your student handout. Determine the scale factor from ABC to A'B'C' by looking at lengths of corresponding sides and distances and write down that scale factor on your student handout as well.
, connect all pairs of corresponding points. Plot a point where all of the lines intersect; this is your center of dilation.
*Mark your center of dilation on your student handout. Determine the scale factor from ABC to A'B'C' by looking at lengths of corresponding sides and distances and write down that scale factor on your student handout as well. 7.
Using the Line tool , connect all pairs of corresponding points. Plot a point where all of the lines intersect; this is your center of dilation.
*Mark your center of dilation on your student handout. Determine the scale factor from ABCD to A'B'C'D' by looking at lengths of corresponding sides and distances and write down that scale factor on your student handout as well.
, connect all pairs of corresponding points. Plot a point where all of the lines intersect; this is your center of dilation.
*Mark your center of dilation on your student handout. Determine the scale factor from ABCD to A'B'C'D' by looking at lengths of corresponding sides and distances and write down that scale factor on your student handout as well. 8.
Dilate triangle ABC by a scale factor of 3 using P as the center of dilation.
Select the Dilate from Point tool 
. Then, select triangle ABC by clicking on the inside of the triangle. Then, select point P. A dialog box will open up asking for your scale factor; type in 3.
*Record your image on your student notetaker.
. Then, select triangle ABC by clicking on the inside of the triangle. Then, select point P. A dialog box will open up asking for your scale factor; type in 3.
*Record your image on your student notetaker. 9.
Dilate ABCD by a scale factor of 1/2 using C as the center of dilation.
Select the Dilate from Point tool . Then, select ABCD by clicking on the inside of the trapezoid. Then, select point C. A dialog box will open up asking for your scale factor; type in 1/2.
*Record your image on your student notetaker.
. Then, select ABCD by clicking on the inside of the trapezoid. Then, select point C. A dialog box will open up asking for your scale factor; type in 1/2.
*Record your image on your student notetaker. 10.
Dilate ABC by a scale factor of 3/2, or 1.5 using P as the center of dilation.
Select the Dilate from Point tool . Then, select ABC by clicking on the inside of the triangle. Then, select point P. A dialog box will open up asking for your scale factor; type in 3/2 or 1.5.
*Record your image on your student notetaker.
. Then, select ABC by clicking on the inside of the triangle. Then, select point P. A dialog box will open up asking for your scale factor; type in 3/2 or 1.5.
*Record your image on your student notetaker. 11. Creating a Dilation
You are going to dilate your own shape.
Using the Polygon tool 
, construct a shape of your choosing. Then, plot a point using the Point tool 
somewhere outside of the shape. Finally, select the Dilate from Point tool . Once you have selected this tool, click somewhere on the inside of your polygon, then select the point you chose. A dialogue box will pop up asking you for your scale factor; type in your desired scale factor and then click okay.
, construct a shape of your choosing. Then, plot a point using the Point tool somewhere outside of the shape. Finally, select the Dilate from Point tool . Once you have selected this tool, click somewhere on the inside of your polygon, then select the point you chose. A dialogue box will pop up asking you for your scale factor; type in your desired scale factor and then click okay. 12.
Map ABC on to XYZ with a dilation.
Using the techniques you learned earlier, determine the location of the center of dilation and the scale factor from ABC to XYZ.
Hints:
*Use the Line tool to connect corresponding points and mark the center of dilation using the Point tool .
*Determine the scale factor by looking at lengths of corresponding side and distances.
*Perform a dilation by using the Dilate from Point tool . After you have selected the tool, select ABC shape by clicking on the inside of it, then select your point, then type in your scale factor. Your image should turn the same color as your preimage.
tool to connect corresponding points and mark the center of dilation using the Point tool .
*Determine the scale factor by looking at lengths of corresponding side and distances.
*Perform a dilation by using the Dilate from Point tool . After you have selected the tool, select ABC shape by clicking on the inside of it, then select your point, then type in your scale factor. Your image should turn the same color as your preimage. 13.
Map ABCD on to WXYZ with a dilation.
Using the techniques you learned earlier, determine the location of the center of dilation and the scale factor from ABC to XYZ.
Hints:
*Use the Line tool to connect corresponding points and mark the center of dilation using the Point tool .
*Determine the scale factor by looking at lengths of corresponding side and distances.
*Perform a dilation by using the Dilate from Point tool . After you have selected the tool, select ABC shape by clicking on the inside of it, then select your point, then type in your scale factor. Your image should turn the same color as your preimage.
tool to connect corresponding points and mark the center of dilation using the Point tool .
*Determine the scale factor by looking at lengths of corresponding side and distances.
*Perform a dilation by using the Dilate from Point tool . After you have selected the tool, select ABC shape by clicking on the inside of it, then select your point, then type in your scale factor. Your image should turn the same color as your preimage. 14.
Map ABCD on to WXYZ with a dilation.
Using the techniques you learned earlier, determine the location of the center of dilation and the scale factor from ABC to XYZ.
Hints:
*Use the Line tool to connect corresponding points and mark the center of dilation using the Point tool .
*Determine the scale factor by looking at lengths of corresponding side and distances.
*Perform a dilation by using the Dilate from Point tool . After you have selected the tool, select ABC shape by clicking on the inside of it, then select your point, then type in your scale factor. Your image should turn the same color as your preimage.
tool to connect corresponding points and mark the center of dilation using the Point tool .
*Determine the scale factor by looking at lengths of corresponding side and distances.
*Perform a dilation by using the Dilate from Point tool . After you have selected the tool, select ABC shape by clicking on the inside of it, then select your point, then type in your scale factor. Your image should turn the same color as your preimage. 15. Creating a dynamic Dilation.
In order to create a dilation that is dynamic like questions 1-4, follow the directions below. You still have a limited tool pallet; however you have access to all of the menus.
Create your own polygon using the polygon tool . Then, using the point tool 
, plot a point away from your polygon; this will serve as your center of dilation.
Select dilate from point tool, and when the dialogue box pops up for you to input your scale factor, type in the letter k instead of a number. You should see an option pop up that says "Create a slider for k"? Click "create sliders."
You will now see a slider up above. I recommend right clicking on it, and under "slider" and adjust the minimum and maximum as need be. Your minimum should be zero; your maximum is up to you.
There are a whole host of menus to access simply by right clicking on various objects. Simple things such as adjusting the colors are fun to play with.
. Then, using the point tool , plot a point away from your polygon; this will serve as your center of dilation.
Select dilate from point tool, and when the dialogue box pops up for you to input your scale factor, type in the letter k instead of a number. You should see an option pop up that says "Create a slider for k"? Click "create sliders."
You will now see a slider up above. I recommend right clicking on it, and under "slider" and adjust the minimum and maximum as need be. Your minimum should be zero; your maximum is up to you.
There are a whole host of menus to access simply by right clicking on various objects. Simple things such as adjusting the colors are fun to play with.