A line segment has endpoints at $(8, 5)$ $(8 ,5 )$ and $(2, 1)$ $(2 ,1 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $- 1$ $- 1$ , 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 $(8, 5)$ $(8 ,5 )$ and $(2, 1)$ $(2 ,1 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $- 1$ $- 1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-02-28T10:04:03

$(- 4, - 8) and (0, - 2)$ $(-4,-8)" and "(0,-2)$

Explanation:

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

$A (8, 5) and B (2, 1)$ $A(8,5)" and "B(2,1)$

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

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

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

$rArrA(8,5)toA'(5,-8)$

$rArrB(2,1)toB'(1,-2)$

$color(blue)"Second transformation"$

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

$• " a point "(x,y)to(x-1,y)$

$rArrA'(5,-8)toA''(4,-8)$

$rArrB'(1,-2)toB''(0,-2)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$rArrA''(4,-8)toA'''(-4,-8)$

$rArrB''(0,-2)toB'''(0,-2)$

$"After all 3 transformations"$

$(8,5)to(-4,-8)" and "(2,1)to(0,-2)$

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A line segment has endpoints at $(8, 5)$ $(8 ,5 )$ and $(2, 1)$ $(2 ,1 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $- 1$ $- 1$ , 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 (8 ,5 )(8,5)(8 ,5 ) and (2 ,1 )(2,1)(2 ,1 ). If the line segment is rotated about the origin by ( 3 pi)/2 3π2( 3 pi)/2 , translated horizontally by - 1 −1 - 1 , 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 $(8, 5)$ $(8 ,5 )$ and $(2, 1)$ $(2 ,1 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $- 1$ $- 1$ , and reflected about the y-axis, what will the line segment's new endpoints be?