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Consider the dilation T(x,y) = (mx,my), where m is a positive number. If m > 1, then T is a radial expansion; if m < 1, then T is a radial contraction. Regardless of the value of m, show that T transforms any segment with endpoints P = (a, b) and Q = (c, d) onto an image segment that is parallel and m times as long

Consider the dilation T(x,y) = (mx,my), where m is a positive number. If m > 1, then T is a radial expansion; if m < 1, then T is a radial contraction. Regardless of the value of m, show that T transforms any segment with endpoints P = (a, b) and Q = (c, d) onto an image segment that is parallel and m times as long

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Consider the dilation T(x,y) = (mx,my), where m is a positive number. If m > 1, then T is a radial expansion; if m < 1, then T is a radial contraction. Regardless of the value of m, show that T transforms any segment with endpoints P = (a, b) and Q = (c, d) onto an image segment that is parallel and m times as long. Hint: vectors might prove easier than the Pythagorean Theorem. 

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