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

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

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Answer 1 · 2018-04-12T04:44:31

$Distance of A from origin after reflection and dilation = 8.6$ $color(purple)("Distance of A from origin after reflection and dilation " = 8.6$

$Distance of B from origin after reflection and dilation = 9.06$ $color(purple)("Distance of B from origin after reflection and dilation " = 9.06$

Explanation:

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

$Reflection rule : reflect thru x = 2, y = - 1, h = 2, k = - 1 . (2 h - x, 2 k - y)$ $"Reflection rule : reflect thru " x = 2, y = -1, h=2, k= -1. (2h-x, 2k-y)$

$A'(x,y) = (2h-x, 2k-y) = (4-1, -2-1) = (3, -3)$

$B'(x,y) = (2h-x, 2k-y) = (4-4, -2-2) = (0, -4)$

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

$A'(x,y) -> A''(x,y) = 2*A'(x,) - C(x,y) = ((6,-6)-(1,1)) = (5,-7)$

$B'(x,y) -> B''(x,y) = 2*B'(x,y) - C(x,y) = ((0,-8)-(1,1)) = (-1,-9)$

$OA'' = sqrt(5^2 + 7^2) = 8.6$

$OB'' = sqrt(15^2 + 9^2) = 9.06$

$color(purple)("Distance of A from origin after reflection and dilation " = 8.6$

$color(purple)("Distance of B from origin after reflection and dilation " = 9.06$

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

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Explanation:

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A line segment goes from (1 ,1 )(1,1)(1 ,1 ) to (4 ,2 )(4,2)(4 ,2 ). The line segment is reflected across x=2x=2x=2, reflected across y=-1y=−1y=-1, and then dilated about (1 ,1 )(1,1)(1 ,1 ) by a factor of 222. How far are the new endpoints from the origin?

1 Answer

Explanation:

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