A line segment has endpoints at $(2, 3)$ $(2 ,3 )$ and $(8, 9)$ $(8 ,9 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $( pi)/2$ , translated vertically by $- 8$ $-8$ , 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 $(2, 3)$ $(2 ,3 )$ and $(8, 9)$ $(8 ,9 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $( pi)/2$ , translated vertically by $- 8$ $-8$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-05-07T10:57:45

$(- 3, 6) and (- 9, 0)$ $(-3,6)" and "(-9,0)$

Explanation:

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

$A (2, 3) and B (8, 9)$ $A(2,3)" and "B(8,9)$

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

$under a rotation about the origin of \frac{π}{2}$ $"under a rotation about the origin of "pi/2$

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

$rArrA(2,3)toA'(-3,2)$

$rArrB(8,9)toB'(-9,8)$

$color(blue)"Second transformation"$

$"under a vertical translation "((0),(-8))$

$• " a point "(x,y)to(x,y-8)$

$rArrA'(-3,2)toA''(-3,-6)$

$rArrB'(-9,8)toB''(-9,0)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$rArrA''(-3,-6)toA'''(-3,6)$

$rArrB''(-9,0)toA'''(-9,0)$

$"After all 3 transformations"$

$(2,3)to(-3,6)" and "(8,9)to(-9,0)$

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A line segment has endpoints at $(2, 3)$ $(2 ,3 )$ and $(8, 9)$ $(8 ,9 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $( pi)/2$ , translated vertically by $- 8$ $-8$ , and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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Math

Humanities

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A line segment has endpoints at (2 ,3 )(2,3)(2 ,3 ) and (8 ,9 )(8,9)(8 ,9 ). If the line segment is rotated about the origin by ( pi)/2 π2( pi)/2 , translated vertically by -8 −8-8 , 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 $(2, 3)$ $(2 ,3 )$ and $(8, 9)$ $(8 ,9 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $( pi)/2$ , translated vertically by $- 8$ $-8$ , and reflected about the x-axis, what will the line segment's new endpoints be?