A line segment has endpoints at $(9, 1)$ $(9 ,1 )$ and $(5, 3)$ $(5 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated vertically 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 $(9, 1)$ $(9 ,1 )$ and $(5, 3)$ $(5 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated vertically by $- 1$ $-1$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-02-27T13:49:52

$(- 9, 2) and (- 5, 4)$ $(-9,2)" and "(-5,4)$

Explanation:

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

$A (9, 1) and B (5, 3)$ $A(9,1)" and "B(5,3)$

$First transformation$ $color(blue)"First transformation"$

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

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

$rArrA(9,1)toA'(-9,-1)$

$rArrB(5,3)toB'(-5,-3)$

$color(blue)"Second transformation"$

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

$• " a point "(x,y)to(x,y-1)$

$rArrA'(-9,-1)toA''(-9,-2)$

$rArrB'(-5,-3)toB''(-5,-4)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$rArrA''(-9,-2)toA'''(-9,2)$

$rArrB''(-5,-4)toB'''(-5,4)$

$"After all 3 transformations"$

$(9,1)to(-9,2)" and "(5,3)to(-5,4)$

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A line segment has endpoints at $(9, 1)$ $(9 ,1 )$ and $(5, 3)$ $(5 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated vertically 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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A line segment has endpoints at (9 ,1 )(9,1)(9 ,1 ) and (5 ,3)(5,3)(5 ,3). If the line segment is rotated about the origin by pi πpi , translated vertically 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 $(9, 1)$ $(9 ,1 )$ and $(5, 3)$ $(5 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated vertically by $- 1$ $-1$ , and reflected about the x-axis, what will the line segment's new endpoints be?