A line segment has endpoints at $(1, 7)$ $(1 ,7 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , 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 $(1, 7)$ $(1 ,7 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-07-03T09:21:54

$(5, - 7) and (7, - 1)$ $(5,-7)" and "(7,-1)$

Explanation:

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

$A = (1, 7) and B = (3, 1)$ $A=(1,7)" and "B=(3,1)$

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

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

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

$A(1,7)toA'(-1,-7)$

$B(3,1)toB'(-3,-1)$

$color(blue)"second transformation"$

$"under a horizontal translation "((-4),(0))$

$• " a point "(x,y)to(x-4,y)$

$A'(-1,-7)toA''(-5,-7)$

$B'(-3,-1)toB''(-7,-1)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

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

$B''(-7,-1)toB'''(7,-1)$

$"After all 3 transformations"$

$(1,7)to(5,-7)" and "(3,1)to(7,-1)$

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A line segment has endpoints at $(1, 7)$ $(1 ,7 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A line segment has endpoints at (1 ,7 )(1,7)(1 ,7 ) and (3 ,1 )(3,1)(3 ,1 ). If the line segment is rotated about the origin by pi π pi , translated horizontally by - 4 −4 - 4 , 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 $(1, 7)$ $(1 ,7 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , and reflected about the y-axis, what will the line segment's new endpoints be?