A line segment has endpoints at (1 ,4 ) and (3 ,4 ). The line segment is dilated by a factor of 6 around (2 ,5 ). What are the new endpoints and length of the line segment?

1 Answer
Alan P.
Oct 17, 2017

New endpoints: (-4,-1), (8,-1)
New line segment length: 12

Explanation:

Note that the distance between the initial line segment end points: (1,4) and (3,4) is color(green)(2) units.
Dilating by a factor of color(magenta)6 will result in a new length of color(magenta)6xxcolor(green)2=color(red)(12)

Consider the vectors from the point of dilation: (2,5) and each of the end points:
{: ("Initial endpoints:",color(white)("xxx"),(1,4),color(white)("xxx"),(3,4)), ("vector from dilation point "(2,5)":",color(white)("xxx"),(-1,-1),color(white)("xxx"),(1,-1)), ("vector after dilation " 6xx":"color(white)("xxx"),,(-6,-6),color(white)("xxx"),(6,-6)), ("new end points:",color(white)("xxx"),(2,5)+(-6,-6),color(white)("xxx"),(2,5)+(6,-6)), (,color(white)("xxx"),=color(red)(""(-4,-1)),color(white)("xxx"),=color(red)(""(8,-1))) :}
enter image source here

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