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

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Feb 10, 2018

New end points coordinates of $A \left(\begin{matrix}2 \\ 1\end{matrix}\right) , B \left(\begin{matrix}18 \\ 5\end{matrix}\right)$

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

#### Explanation:

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

$\vec{A ' C} = 4 \cdot \vec{A C}$ or $a ' = 4 a - 3 c$

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

$\vec{B ' C} = 4 \cdot \vec{B C}$ or $b ' = 4 b - 3 c$

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

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