A line segment has endpoints at $(75 ,8 )$ and $(2 , 1)$ . The line segment is dilated by a factor of $2$ around $(4 , 5)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T03:10:02

$color(crimson)("New coordinates are " (146,11), (0, -3)$

$color(crimson)("Length of the line segment '" = sqrt((146-0)^2 + (11--3)^2) ~~ 146.6697$

$A(75,8), B(2,1)," about point " D (4,5), " dilation factor "2$

$A'((x),(y)) =(2)a - (1)d =(2)*((75),(8)) - (1)*((4),(5)) = ((146),(11))$

$B'((x),(y)) = (2)b - (1)d = (2)*((2),(1)) - (1)*((4),(5)) = ((0),(-3))$

$color(crimson)("New coordinates are " (146,11), (0, -3)$

$color(crimson)("Length of the line segment '" = sqrt((146-0)^2 + (11--3)^2) ~~ 146.6697$

A line segment has endpoints at (75 ,8 )(75 ,8 ) and (2 , 1)(2 , 1). The line segment is dilated by a factor of 2 2 around (4 , 5)(4 , 5). What are the new endpoints and length of the line segment?