Dilations and Circles: Preserving Properties and Mapping Radii, Study notes of Pre-Calculus

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1. Dilate circle O by a scale factor r = 1/2 using a compass. The center of dilation is the center of the circle.

O

2. Given points O, S, and T below: a. Construct circle T, radius TS. b. Perform DO,2 (Circle T).

3. Using your compass, dilate circle C with radius CA from center O with a scale factor r = 2. CA ___ C'A' and C'A' = ____. C O A
4. The diagram below shows the dilation of circle O. A dilation with center D was performed using scale factor r. Circle one: r > 1 or 0 < r < 1. Find point W on circle O that is mapped to point W' on circle O'. OW ____O'W' D O^ O' W'

A'

A

A"

a. Circle A' is a dilation of circle A using the origin as the center of dilation. What is the scale factor? b. Circle A" is a dilation of A' using the origin as the center of dilation. What is the scale factor? c. Dilate circle A' using a scale factor of 1.5. Let's Sum it Up! Dilation Theorem for rays: A dilation maps a ray to a ray sending the endpoint to the endpoint. Dilation Theorem for lines: A dilation maps a line to a line. If the center O of the dilation lies on the line or if the scale factor r of the dilation is equal to 1, then the dilation maps the line to the same line. Otherwise, the dilation maps the line to a parallel line. Dilation Theorem for circles: A dilation maps a circle to a circle, and maps the center to the center.

1. Using your compass, dilate circle C with radius CA from center O with a scale factor r = 1/2. A C O
2. The larger circle is a dilation of the smaller circle. Find the center of dilation O. Name: ____________________ CC Geometry H Date: _____________ HW # C' C A
3. Given points M, T, and O below: a) Draw line segment MT. b) Dilate MT from O using scale factor r = 2. Label as M'T'. c) Draw circle T with radius TM. d) Dilate circle T with radius TM from O using scale factor r = 2. O M (^) T