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

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Answer 1 · 2016-03-08T05:25:45

New endpoints $(7/4, 17/4)$ and $(9/4, 4)$
New Length $l=sqrt5/4$

First Endpoint $(x_1, y_1)$
For $x_1:$

$(2-x_1)/(2-1)=1/4$

$x_1=7/4$

For $y_1:$

$(5-y_1)/(5-2)=1/4$

$y_1=17/4$

$(7/4, 17/4)$

Second Endpoint $(x_2, y_2)$

For $x_2:$

$(2-x_2)/(2-3)=1/4$

$x_2=9/4$

For $y_2:$

$(5-y_2)/(5-1)=1/4$

$y_2=4$

$(9/4, 4)$

Length $l=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$l=sqrt((9/4-7/4)^2+(4-17/4)^2)$

$l=sqrt((2/4)^2+(-1/4)^2)$

$l=sqrt5/4$

God bless... I hope the explanation is useful

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