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

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Answer 1 · 2018-04-12T04:18:25

$"Distance of the two points from origin after dilation and reflection "$
$color(blue)( 3.16, 4.24)$

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

$A'(x,) = 2 * A(x,y) - C(x,y) =( (4,6) - (1,1)) = (3,5)$

$B'(x,) = 2 * B(x,y) - C(x,y) =( (8,2) - (1,1)) = (7,1)$

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

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

$B''(x,y) = (2 * 2 - 7), (2*-1 - 1) = (-3, -3)$

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

$B''O = sqrt(3^2 + 3^2) = 4.24$

A line segment goes from (2 ,3 )(2 ,3 ) to (4 ,1 )(4 ,1 ). 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=2x=2 and y=-1y=-1, in that order. How far are the new endpoints from the origin?