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The properties of dilations on circles, focusing on how dilations map circles onto other circles while preserving certain properties. Topics include determining which hexagon property is not preserved under a dilation, calculating scale factors, and understanding how dilations affect circles' centers and radii. Students will also learn about the Dilation Theorem for circles.
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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.