A line segment has endpoints at $(2, 1)$ $(2 ,1 )$ and $(6, 2)$ $(6 ,2 )$ . 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 · 2018-02-10T09:02:22

New end points coordinates of $A ((2),(1)), B ((18),(5))$

length of line segment $~~ color(green)(16.49$

Given : A(2,1), B(6,2), 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 $a' = 4a - 3c$

$a' = 4((2),(1)) - 3 ((2),(1)) = ((8),(4)) - ((6),(3)) = color(brown)(((2),(1))$

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

$b' = 4((6),(2)) - 3 ((2),(1)) = ((24),(8)) - ((6),(3)) = color(brown)( ((18),(5))$

Length of the line segment using distance formula,

$vec(A'B') = sqrt((2-18)^2 + (1-5)^2) ~~ color(green)(16.49$

A line segment has endpoints at (2 ,1 )(2,1)(2 ,1 ) and (6 ,2 )(6,2)(6 ,2 ). 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?