A line segment has endpoints at $(1, 4)$ $(1 ,4 )$ and $(3, 5)$ $(3 ,5 )$ . The line segment is dilated by a factor of $6$ $6$ around $(2, 5)$ $(2 ,5 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T05:15:25

$New end points are (- 4, - 1), (8, 5)$ $color(green)("New end points are " (-4,-1), (8,5)$

$Length of the line segment \approx 13.4164$ $color(green)("Length of the line segment " ~~ 13.4164$

$A (1, 4), B (3, 5), about point D (2, 5), dilation factor 6$ $A(1,4), B(3,5), " about point " D (2,5), " dilation factor " 6$

$A'((x),(y)) =(6)a - (5)d =(6)* ((1),(4)) - (5)*((2),(5)) = ((-4),(-1))$

$B'((x),(y)) = (6)b - (5)d = (6)* ((3),(5)) - (5)*((2),(5)) = ((8),(5)$

$color(green)("New end points are " (-4,-1), (8,5)$

$color(green)("Length of the line segment " = sqrt((-4-8)^2 + (-1-5)^2) ~~ 13.4164$

A line segment has endpoints at (1 ,4 )(1,4)(1 ,4 ) and (3 ,5 )(3,5)(3 ,5 ). The line segment is dilated by a factor of 6 66 around (2 ,5 )(2,5)(2 ,5 ). What are the new endpoints and length of the line segment?