A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(8, 2)$ $(8 ,2 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $- 1$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(8, 2)$ $(8 ,2 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $- 1$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-06-24T22:12:40

$(- 8, 5) and (- 9, 2)$ $(-8,5)" and "(-9,2)$

Explanation:

$since there are 3 transformations to be performed label$ $"since there are 3 transformations to be performed label"$
$the endpoints$ $"the endpoints"$

$A = (7, 5) and B = (8, 2)$ $A=(7,5)" and "B=(8,2)$

$first transformation$ $color(blue)"first transformation"$

$under a rotation about the origin of π$ $"under a rotation about the origin of "pi$

$∙ a point (x, y) \to (- x, - y)$ $• " a point "(x,y)to(-x,-y)$

$A(7,5)toA'(-7,-5)$

$B(8,2)toB'(-8,-2)$

$color(blue)"second transformation"$

$"under a horizontal translation "((-1),(0))$

$• " a point "(x,y)to(x-1,y)$

$A'(-7,-5)toA''(-8,-5)$

$B'(-8,-2)toB''(-9,-2)$

$color(blue)"third transformation"$

$"under a reflection in the x-axis"$

$• " a point " (x,y)to(x,-y)$

$A''(-8,-5)toA'''(-8,5)$

$B''(-9,-2)toB'''(-9,2)$

$"After all 3 transformations"$

$(7,5)to(-8,5)" and "(8,2)to(-9,2)$

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A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(8, 2)$ $(8 ,2 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $- 1$ , and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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Humanities

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A line segment has endpoints at (7 ,5 )(7,5)(7 ,5 ) and (8 ,2 )(8,2)(8 ,2 ). If the line segment is rotated about the origin by pi π pi , translated horizontally by - 1 −1 - 1 , and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(8, 2)$ $(8 ,2 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $- 1$ , and reflected about the x-axis, what will the line segment's new endpoints be?