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

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Answer 1 · 2018-03-03T02:05:13

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

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

Given $A (3,2), B (2,4)$ Rotated about $C(1,1)$ 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

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

A line segment has endpoints at (3 ,2 )(3,2)(3 ,2 ) and (2 , 4)(2,4)(2 , 4). The line segment is dilated by a factor of 4 44 around (1 , 1)(1,1)(1 , 1). What are the new endpoints and length of the line segment?