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

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Answer 1 · 2018-04-12T08:24:33

$color(violet)("Distance of A & B from origin after reflection and dilation " 9, 12.04 " respy."$

$A (1,2), B (4,1)," reflected across " x = -3, y = 1$

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

$A'(x,y) = A(2h-x, 2k-y) = (-6-1, 4-2) = (-7,2)$

$B'(x,y) = B(2h-x, 2k-y) = (-6-4, 4-1) = (-10,3)$

Points A' & B' dilated about C(2,2) by a factor of 2.

$A'(x,y) -> A''(x,y) = A'(x,y) - C(x,y) = ((-7,2) - (2,2)) = (-9,0)$

$B'(x,y) -> B''(x,y) = B'(x,y) - C(x,y) = ((-10,3) - (2,2)) = (-12,1)$

$OA' = 9, OB' = sqrt(-12^2 + 1^2 = 12.04$

A line segment goes from (1 ,2 )(1 ,2 ) to (4 ,1 )(4 ,1 ). The line segment is reflected across x=-3x=-3, reflected across y=1y=1, and then dilated about (2 ,2 )(2 ,2 ) by a factor of 33. How far are the new endpoints from the origin?