IM 8.2.5 Lesson: More Dilations

Explore the applet and observe the dilation of triangle [math]ABC[/math]. The dilation always uses center [math]P[/math], but you can change the scale factor. What connections can you make between the scale factor and the dilated triangle?[br]
Your teacher will give you either a [i]problem card[/i] or a [i]data card[/i]. Do not show or read your card to your partner.[br][br][table][tr][td]If your teacher gives you the [i]problem card[/i]:[/td][td]If your teacher gives you the [i]data card[/i]:[/td][/tr][tr][td][list=1][*]Silently read your card and think about what [br]information you need to be able to answer the [br]question.[br][/*][*]Ask your partner for the specific information that [br]you need.[br][/*][*]Explain how you are using the information to [br]solve the problem.[br]Continue to ask questions until you have enough [br]information to solve the problem.[br][/*][*]Share the [i]problem card [/i]and solve the problem[br]independently.[br][/*][*]Read the [i]data card[/i] and discuss your reasoning.[br][/*][/list][/td][td][list=1][*]Silently read your card.[/*][*]Ask your partner [i]“What specific information do you [br]need?”[/i] and wait for them to [i]ask[/i] for information.[br]If your partner asks for information that is not on [br]the card, do not do the calculations for them. Tell [br]them you don’t have that information.[/*][*]Before sharing the information, ask “[i]Why do you [br]need that information?[/i]” Listen to your partner’s [br]reasoning and ask clarifying questions.[/*][*]Read the [i]problem card[/i] and solve the problem independently.[/*][*]Share the [i]data card[/i] and discuss your reasoning.[/*][/list][br][/td][/tr][/table][br]Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.[br]
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 1/2 and center D.
[br][img]data:image/png;base64,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[/img][br]What would the image of triangle ABC look like under a dilation with scale factor 0?
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.[br][br]
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.

IM 8.2.5 Practice: More Dilations

Quadrilateral ABCD is dilated with center (0,0), taking B to B'. Draw A'B'C'D'.
Triangles B and C have been built by dilating Triangle A. Find the center of dilation.
Triangle [math]B[/math] is a dilation of [math]A[/math] with approximately what scale factor?
Triangle [math]A[/math] is a dilation of [math]B[/math] with approximately what scale factor?
Triangle [math]B[/math] is a dilation of [math]C[/math] with approximately what scale factor?
Here is a triangle. Draw the dilation of triangle ABC, with center (0,0), and scale factor of 2. Label this triangle A'B'C'.
On the triangle from above, draw the dilation of triangle [math]ABC[/math], with center [math](0,0)[/math], and scale factor of [math]\frac{1}{2}[/math]. Label this triangle [math]A''B''C''[/math]. Is [math]A''B''C''[/math] a dilation of triangle [math]A'B'C'[/math]? If yes, what are the center of dilation and the scale factor?
Triangle [math]DEF[/math] is a right triangle, and the measure of angle [math]D[/math] is [math]28°[/math]. What are the measures of the other two angles?

Information