IM 8.2.2 Lesson: Circular Grid

Author:GeoGebra Classroom Activities, IM 6 – 8 Math, IM 6 - 8 Math

What do you notice? What do you wonder?

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

1. Draw four points on the smaller circle using the Point on Object tool. 2. Draw the rays from through each of those four points. Select the Ray tool, then point , and then the second point. 3. Mark the intersection points of the rays and Circle d by selecting the Intersect tool and clicking on the point of intersection. 4. Complete the table. In the row labeled S, write the distance between

and the point on the smaller circle in grid units. In the row labeled L, write the distance between

and the corresponding point on the larger circle in grid units. Measure the distances between pairs of points by selecting the Distance tool, and then clicking on the two points.

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

Here is a polygon ABCD. Dilate each vertex of polygon ABCD using P as the center of dilation and a scale factor of 2. Draw segments between the dilated points to create a new polygon.

What are some things you notice about the new polygon?

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

Dilate each vertex of polygon using as the center of dilation and a scale factor of . What do you notice about this new polygon?

Suppose is a point not on line segment . Let be the dilation of line segment using as the center with scale factor 2. Experiment using a circular grid to make predictions about whether each of the following statements must be true, might be true, or must be false. is twice as long

Select all that apply

A
must be true
B
might be true
C
must be false

Check my answer (3)

The point is on .

Select all that apply

A
must be true
B
might be true
C
must be false

Check my answer (3)

is five units longer than

Select all that apply

A
must be true
B
might be true
C
must be false

Check my answer (3)

and intersect.

Select all that apply

A
must be true
B
might be true
C
must be false

Check my answer (3)

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.)

IM 8.2.2 Lesson: Circular Grid

What do you notice? What do you wonder?

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

Here is a polygon ABCD. Dilate each vertex of polygon ABCD using P as the center of dilation and a scale factor of 2. Draw segments between the dilated points to create a new polygon.

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.)

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