A line segment goes from $(5 ,8 )$ to $(4 ,2 )$ . The line segment is reflected across $x=-3$ , reflected across $y=-5$ , and then dilated about $(2 ,0 )$ by a factor of $2$ . How far are the new endpoints from the origin?

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Answer 1 · 2017-06-05T22:53:56

$2 sqrt 202 and 4 sqrt 34$

$A_1 = (5, 8) ; B_1 = (4, 2)$

$-3 + x mapsto -3 - x$
$-3 + x+3 mapsto -3 - x - 3 = -6 -x$

$A_2 = (-6 -5, 8) ; B_2 = (-6 -4, 2)$

$-5 + y mapsto -5 - y$
$-5 + y + 5 mapsto -5 - y - 5 = -10 -y$

$A_3 = (-11, -10-8) ; B_3 = (-10, -10-2)$

What is to dilate the line about (2, 0) by a factor of 2?

I suppose $(x,y) mapsto (2x, y)$

$A_4 = (-11 * 2, -18) ; B_4 = (-10 * 2, -12)$

$|A_4|^2 = 22^2 + 18^2$

$|B_4|^2 = 20^2 + 12^2$

A line segment goes from (5 ,8 )(5 ,8 ) to (4 ,2 )(4 ,2 ). The line segment is reflected across x=-3x=-3, reflected across y=-5y=-5, and then dilated about (2 ,0 )(2 ,0 ) by a factor of 22. How far are the new endpoints from the origin?