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

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Answer 1 · 2018-02-05T08:41:32

New end points $color(brown)((-2, -7)$ & $color(brown)((6, -11)$

Length of the line segment $color(green)(d ~~ 8.94)$

Given : End points A(1,2), B (3,1), Center of dilation C(2,5) and dilation factor 4

Let A' and B' be the new end points after dilation.

$bar(CA') = 4 * bar(CA)$

$a' - c = 4 * (a - c)$

$a' = 4a - 3c$

$=>4((1),(2)) -3((2),(5))$

$=>((4),(8)) - ((6),(15)) = ((-2),(-7))$

$color(brown)(A' (-2, -7)$

$bar(CB') = 4 * bar(CB)$

$b' - c = 4(b-c)$

$b' = 4b - 3c$

$=> 4 ((3),(1)) - 3((2),(5))$

$=>((12),(4)) - ((6),(15)) = ((6),(-11))$

$color(brown)(B' (6, -11)$

Using distance formula we can find the length A'B'

$bar(A'B') = sqrt((6-(-2))^2 + ((-11) - (-7))^2) = sqrt(8^2 + 4^2) ~~ color(green)(8.94$ corrected to two decimal points

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