A line segment has endpoints at $(9 ,2 )$ and $(7 , 4)$ . The line segment is dilated by a factor of $4$ around $(1 , 5)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T03:03:40

$color(orange)("New coordinates are " (33,-7), (-25, 1)$

$color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137$

$A(8,4), B(9,2), " about point " D (1,5), " dilation factor "4$

$A'((x),(y)) =(4)a - (3)d =(4)*((9),(2)) - (3)*((1),(5)) = ((33),(-7))$

$B'((x),(y)) = (4)b - (3)d = (4)*((7),(4)) - (3)*((1),(5)) = ((25),(1))$

$color(orange)("New coordinates are " (33,-7), (-25, 1)$

$color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137$

A line segment has endpoints at (9 ,2 )(9 ,2 ) and (7 , 4)(7 , 4). The line segment is dilated by a factor of 4 4 around (1 , 5)(1 , 5). What are the new endpoints and length of the line segment?