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Unit 2 - Lesson 2 - Grade 8: Illustrative Mathematics

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11 Questions
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Grade 8 Unit 2
Lesson 2: Circular Grid
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 2
Lesson 2: Circular Grid
CC BY 2021 Illustrative Mathematics®
Lesson: Circular Grid

Notice and Wonder: Concentric Circles (Warm Up)

1.

What do you notice? What do you wonder?

A Droplet on the Surface

The larger Circle d is a dilation of the smaller Circle c.
P is the center of dilation.
2.

  • Draw four points on the smaller circle (not inside the circle!), and label them E, F, G, and H.
  • Draw the rays from P through each of those four points.
  • Label the points where the rays meet the larger circle E', F', G', and H'.

3.

Complete the table. In the row labeled c, write the distance between P and the point on the smaller circle in grid units. In the row labeled d, write the distance between P and the corresponding point on the larger circle in grid units.

4.

The center of dilation is point P. What is the scale factor that takes the smaller circle to the larger circle? Explain your reasoning.

Quadrilateral on a Circular Grid

Here is a polygon ABCD.
5.

  • Dilate each vertex of polygon ABCD using P as the center of dilation and a scale factor of 2. Label the image of A as A', and label the images of the remaining three vertices as B', C', and D'.
  • Draw segments between the dilated points to create polygon A', B', C', D'.

6.

What are some things you notice about the new polygon?

7.

Choose a few more points on the sides of the original polygon and transform them using the same dilation. What do you notice?

8.

Dilate each vertex of polygon ABCD using P as the center of dilation and a scale factor of 1/2. Label the image of A as E, the image of B as F, the image of C as G and the image of D as H. What do you notice about polygon EFGH ?

A Quadrilateral and Concentric Circles (Optional)

9.

Dilate polygon EFGH using Q as the center of dilation and a scale factor of 1/3. The image of F is already shown on the diagram. (You may need to draw more rays from Q in order to find the images of other points.)

Cool Down: Dilating Points on a Circular Grid

Dilating Points on a Circular Grid

10.

Dilate A using P as the center of dilation and a scale factor of 3. Label the new point A'.

11.

Dilate B using P as the center of dilation and a scale factor of 2. Label the new point B'.