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

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Answer 1 · 2018-04-12T08:09:39

$color(purple)("Distances of A & B after dilation and reflection "$

$color(green)(9.4868, 1.4142 " respy."$

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

$A(x,y) -> A'(x,y) = 2* A(x,y) - C(x,y) = (2*(3,2) - (1,1)) = (5,3)$

$B(x,y) -> B'(x,y) = 2* B(x,y) - C(x,y) = (2*(1,3) - (1,1)) = (1,5)$

$"Reflection Rule : reflect thru " x = 1, y = -3; h=1, k= -3; (2h-x, 2k-y)$

$A''(x,y) = A'((2h - x), (2k - y)) = (2-5, -6-3) = (-3, -9)$

$B''(x,y) = B'((2h - x), (2k - y)) = (2-1, -6+5) = (1, -1)$

$OA'' = sqrt(-3^2 + -9^2) = 9.4868$

$OB'' = sqrt(1^2 + -1^2) = 1.4142$

A line segment goes from (3 ,2 )(3 ,2 ) to (1 ,3 )(1 ,3 ). The line segment is dilated about (1 ,1 )(1 ,1 ) by a factor of 22. Then the line segment is reflected across the lines x=1x=1 and y=-3y=-3, in that order. How far are the new endpoints from the origin?