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

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Mar 3, 2018

New endpoints color(red)(A’ (8,4), B’(4,12)

Length of the new line segment color(purple)(vec(A’B’) ~~ 8.9443

#### Explanation:

Given $A \left(3 , 2\right) , B \left(2 , 4\right)$ Rotated about $C \left(1 , 1\right)$ by a factor of 4.

To find the new endpoints and the length of the line segment.

vec(A’C) = 4 * vec(AB)

a’((x),(y)) -=c((1),(1)) = 4 * ((3),(2)) - 4 * ((1),(1))

a’((x),(y)) = 4 * ((3),(2)) - 3 * ((1),(1)) = ((12),(8)) - ((4),(4)) = ((8),(4))

Similarly,

b’((x),(y)) = = 4 * ((2),(4)) - 3 * ((1),(1)) = ((8),(16)) - ((4),(4)) = ((4),(12))

Length of the new line segment

vec(A’B’) = sqrt((4-8)^2 + (4-12)^2) ~~ color (purple)(8.9443

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