A line segment goes from $(3, 1)$ $(3 ,1 )$ to $(2, 4)$ $(2 ,4 )$ . The line segment is dilated about $(2, 2)$ $(2 ,2 )$ by a factor of $3$ $3$ . Then the line segment is reflected across the lines $x = 4$ $x = 4$ and $y = - 1$ $y=-1$ , in that order. How far are the new endpoints form the origin?

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Answer 1 · 2018-04-12T04:32:06

$Distances of A and B from origin after dilation and reflection$ $color(indigo)("Distances of A and B from origin after dilation and reflection "$

$3.16, 12.65 respectively$ $color(indigo)(3.16, 12.65 " respectively"$

$A (3, 1), B (2, 4), dilated about C(2,2) by a factor of 3$ $A (3,1), B (2,4), " dilated about C(2,2) by a factor of 3"$

$A' (x,y) =3 * A(x,y) - C (x,y) =(( 9 ,3) - (2,2)) = (7,1)$

$B'(x,y) = 3 ^ B (x,y) - C(x,y) = ((6,12) - (2,2)) = (4,10)$

$color(brown)("reflect thru " x = 4, y = -1, h=4, k= -1. (2h-x, 2k-y)"$

$A''(x,y) = (2h-x, 2k-y) = ((8 - 7), (-2-1)) = (1,-3)$

$"similarly " B''(x,y) = ((8-4),(-2-10)) = (4, -12)$

$bar(A''O) = sqrt(1^2 + 3^2) = sqrt 10 = 3.16$

$bar(B''O) = sqrt(4^2 + 12^2) = sqrt 160 = 12.65$

A line segment goes from (3 ,1 )(3,1)(3 ,1 ) to (2 ,4 )(2,4)(2 ,4 ). The line segment is dilated about (2 ,2 )(2,2)(2 ,2 ) by a factor of 333. Then the line segment is reflected across the lines x = 4x=4x = 4 and y=-1y=−1y=-1, in that order. How far are the new endpoints form the origin?