IM 8.2.4 Lesson: Dilations on a Square Grid

Point [math]C[/math] is the dilation of point [math]B[/math] with center of dilation [math]A[/math] and scale factor [i][math]s[/math][/i]. Estimate[i] [math]s[/math][/i]. Be prepared to explain your reasoning.
Find the dilation of quadrilateral ABCD with center P and scale factor 2.
Find the dilation of triangle QRS with center T and scale factor 2.
Find the dilation of triangle QRS with center T and scale factor 1/2.
Match number cards with letter cards. One of the number cards will not have a match. For this card, you’ll need to draw an image in the next app.
One of the number cards will not have a match. Draw the image here.
The image of a circle under dilation is a circle when the center of the dilation is the center of the circle.
[size=150]What happens if the center of dilation is a point on the circle? Using center of dilation [math](0,0)[/math] and scale factor 1.5, dilate the circle shown on the diagram. This diagram shows some points to try dilating. [/size]

IM 8.2.4 Practice: Dilations on a Square Grid

Triangle [math]ABC[/math] is dilated using [math]D[/math] as the center of dilation with scale factor 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[/img][br]The image is triangle [math]A'B'C'[/math]. Clare says the two triangles are congruent because their angle measures are the same. Do you agree? Explain how you know. 
Sketch the image of quadrilateral PQRS under the following dilation: The dilation centered at R with scale factor 2.
Sketch the image of quadrilateral PQRS under the following dilation: The dilation centered at O with scale factor 1/2.
Sketch the image of quadrilateral PQRS under the following dilation: The dilation centered at S with scale factor 1/2.
The diagram shows three lines with some marked angle measures. Find the missing angle measures marked with question marks.
Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q, using the app to help.
Point [math]B[/math] has coordinates [math](-2,-5)[/math]. After a translation 4 units down, a reflection across the [math]y[/math]-axis, and a translation 6 units up, what are the coordinates of the image?[br][br]Use the coordinate plane below, if needed

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