How Do Dilations Map Lines, Rays, and Circles?
a. Is a dilated ray still a ray? If the ray is transformed under a dilation, explain how.
b. Dilate the 𝑃𝑄 by a scale factor of 2 from center O.
i. Is the figure 𝑃′𝑄′ a ray?
ii. How, if at all, has the ray 𝑃𝑄 been transformed?
iii. Will a ray always be mapped to a ray? Explain how you know
Will a dilation about center 𝑂 and scale factor 𝑟 = 1 map 𝑃𝑄 to 𝑃′𝑄′? Explain.
The line that contains 𝑃𝑄 does not contain point 𝑂. Does a dilation about center 𝑂 and scale factor 𝑟 ≠ 1 map every point of 𝑃𝑄 onto a point of 𝑃′𝑄′?
The line that contains 𝑃𝑄 contains point 𝑂. Does a dilation about center 𝑂 and scale factor 𝑟 map 𝑃𝑄 to 𝑃′𝑄′?
a. Examine the case where the endpoint 𝑃 of 𝑃𝑄 coincides with the center 𝑂 of the dilation.
b. Examine the case where the endpoint 𝑃 of 𝑃𝑄 is between 𝑂 and 𝑄 on the line containing 𝑂, 𝑃, and 𝑄.
c. Examine the remaining case where the center 𝑂 of the dilation and point 𝑄 are on the same side of 𝑃 on the line containing 𝑂, 𝑃, and 𝑄.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.