A line segment has endpoints at $(2, 1)$ $(2 , 1)$ and $(7, 6)$ $(7 ,6)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 3$ $-3$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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A line segment has endpoints at $(2, 1)$ $(2 , 1)$ and $(7, 6)$ $(7 ,6)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 3$ $-3$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-06-16T18:38:28

$(5, - 1) and (10, - 6)$ $(5,-1)" and "(10,-6)$

Explanation:

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

$A = (2, 1) and B = (7, 6)$ $A=(2,1)" and "B=(7,6)$

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

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

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

$A(2,1)toA'(-2,-1)$

$B(7,6)toB'(-7,-6)$

$color(blue)"second transformation"$

$"under a horizontal translation "((-3),(0))$

$• " a point "(x,y)to(x-3,y)$

$A'(-2,-1)toA''(-5,-1)$

$B'(-7,-6)toB''(-10,-6)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$A''(-5,-1)toA'''(5,-1)$

$B''(-10,-6)toB'''(10,-6)$

$"After all 3 transformations"$

$(2,1)to(5,-1)" and "(7,6)to(10,-6)$

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A line segment has endpoints at $(2, 1)$ $(2 , 1)$ and $(7, 6)$ $(7 ,6)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 3$ $-3$ , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at (2 , 1)(2,1)(2 , 1) and (7 ,6)(7,6)(7 ,6). If the line segment is rotated about the origin by pi πpi , translated horizontally by -3 −3-3 , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at $(2, 1)$ $(2 , 1)$ and $(7, 6)$ $(7 ,6)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 3$ $-3$ , and reflected about the y-axis, what will the line segment's new endpoints be?