A line segment has endpoints at $(1, 6)$ $(1 ,6 )$ and $(5, 8)$ $(5 ,8 )$ . The line segment is dilated by a factor of $4$ $4$ around $(2, 1)$ $(2 ,1 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-10T09:09:16

New end points $A' ((-2),(21)), B'((14),(29))$

Line segment length $~~ color(green)(28.64$

Given : A(1,6), B(5,8), dilated around C(2,1), dilation factor 4

To find the end points of the line segment and its length

$vec(A'C) = 4 * vec(AC)$ or $a' = 4a - 3c$

$a' = 4((1),(6)) - 3 ((2),(1)) = ((4),(24)) - ((6),(3)) = color(brown)(((-2),(21))$

$vec(B'C) = 4 * vec(BC)$ or $b' = 4b - 3c$

$b' = 4((5),(8)) - 3 ((2),(1)) = ((20),(32)) - ((6),(3)) = color(brown)( ((14),(29))$

Length of the line segment using distance formula,

$vec(A'B') = sqrt((-2-14)^2 + (3-29)^2) ~~ color(green)(28.64$

A line segment has endpoints at (1 ,6 )(1,6)(1 ,6 ) and (5 ,8 )(5,8)(5 ,8 ). The line segment is dilated by a factor of 4 44 around (2 ,1 )(2,1)(2 ,1 ). What are the new endpoints and length of the line segment?