A line segment has endpoints at $(7, 2)$ $(7 ,2 )$ and $(3, 2)$ $(3 , 2 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi ) /2$ , translated vertically 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 $(7, 2)$ $(7 ,2 )$ and $(3, 2)$ $(3 , 2 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi ) /2$ , translated vertically by $- 4$ $-4$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2017-12-31T09:54:51

$(- 2, - 11) and (- 2, - 7)$ $(-2,-11)" and "(-2,-7)$

Explanation:

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

$A (7, 2) and B (3, 2)$ $A(7,2)" and "B(3,2)$

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

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

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

$rArrA(7,2)toA'(2,-7)$

$rArrB(3,2)toB'(2,-3)$

$color(blue)"second transformation"$

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

$• " a point "(x,y)to(x,y-4)$

$rArrA'(2,-7)toA''(2,-11)$

$rArrB'(2,-3)toB''(2,-7)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$rArrA''(2,-11)toA'''(-2,-11)$

$rArrB''(2,-7)toB'''(-2,-7)$

$"after all 3 transformations"$

$(7,2)to(-2,-11)" and "(3,2)to(-2,-7)$

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A line segment has endpoints at $(7, 2)$ $(7 ,2 )$ and $(3, 2)$ $(3 , 2 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi ) /2$ , translated vertically 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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A line segment has endpoints at (7 ,2 )(7,2)(7 ,2 ) and (3 , 2 )(3,2)(3 , 2 ). If the line segment is rotated about the origin by (3 pi ) /2 3π2(3 pi ) /2 , translated vertically 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 $(7, 2)$ $(7 ,2 )$ and $(3, 2)$ $(3 , 2 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi ) /2$ , translated vertically by $- 4$ $-4$ , and reflected about the y-axis, what will the line segment's new endpoints be?