Circular Grid

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Introduction to Circular Griding.

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

  • Draw four points on the smaller circle using the Point on Object tool .​
  • Draw rays from  each point through each of the other points using the Ray tool .​ In the end, you should have 3 lines passing through each point to the larger circle.
  • Mark the intersection points of the rays and Circle d by selecting the Intersect tool and clicking on the point of intersection.​
  • 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 P. What is the scale factor that takes the smaller circle to the larger circle? Explain your reasoning.

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Introduction to 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.

(1). What are some things you notice about the new polygon?

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

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

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Solving Problems on Dilation.

(1). Here are Circles c and d. Point O is the center of dilation, and the dilation takes Circle c to Circle d. Plot a point on Circle c. Label the point P. Plot where P goes when the dilation is applied.

(2). Plot a point on Circle d above. Label the point Q. Plot a point that the dilation takes to Q.

(3). Here below is triangle ABC. Dilate each vertex of triangle ABC using P as the center of dilation and a scale factor of 2. Draw the triangle connecting the three new points. Then, do the same using a scale factor of .

(1). Measure the longest side of each of the three triangles. What do you notice?

(2). Measure the angles of each triangle. What do you notice?

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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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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.

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