A line segment has endpoints at $(3 ,2 )$ and $(2 , 5)$ . The line segment is dilated by a factor of $4$ around $(2 , 3)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-12T11:22:20

New coordinates of end points $color(purple)(((6),(-1)), ((2),(11))$

Length of the line segment $vec(A'B') = ~~ color(green)(12.65$

Existing points A (3,2), B (2,5). Dilated around C (2,3) by factor 4

To find new end points and length of segment.

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

$a' = 4 ((3),(2)) - 3 ((2),(3)) = ((12),(8)) - ((6),(9)) => ((6),(-1))$

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

$b' = 4((2),(5)) - 3 ((2),(3)) = ((8),(20)) - ((6),(9)) = ((2),(11))$

$vec(A'B') = sqrt((2-6)^2 + (11+1)^) = sqrt160 ~~ color(green)(12.65$

A line segment has endpoints at (3 ,2 )(3 ,2 ) and (2 , 5)(2 , 5). The line segment is dilated by a factor of 4 4 around (2 , 3)(2 , 3). What are the new endpoints and length of the line segment?