A line segment has endpoints at $(4, 2)$ $(4 ,2 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , 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 $(4, 2)$ $(4 ,2 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-07-28T07:36:29

$(4, 4) and (5, 5)$ $(4,4)" and "(5,5)$

Explanation:

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

$A = (4, 2) and B = (5, 3)$ $A=(4,2)" and "B=(5,3)$

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

$under a rotation about the origin of \frac{3 π}{2}$ $"under a rotation about the origin of "(3pi)/2$

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

$A(4,2)toA'(2,-4)$

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

$color(blue)"second transformation"$

$"under a horizontal transformation "((2),(0))$

$• " a point "(x,y)to(x+2,y)$

$A'(2,-4)toA''(4,-4)$

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

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$A''(4,-4)toA'''(4,4)$

$B''(5,-5)toB'''(5,5)$

$"After all 3 transformations"$

$(4,2)to(4,4)" and "(5,3)to(5,5)$

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A line segment has endpoints at $(4, 2)$ $(4 ,2 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , 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 (4 ,2 )(4,2)(4 ,2 ) and (5 ,3 )(5,3)(5 ,3 ). If the line segment is rotated about the origin by ( 3 pi)/2 3π2( 3 pi)/2 , translated horizontally by 2 2 2 , 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 $(4, 2)$ $(4 ,2 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?