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

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Answer 1 · 2017-08-05T14:05:56

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

Explanation:

$since there are 3 transformations to be performed name the$ $"Since there are 3 transformations to be performed name the "$
$endpoints A(1,2) and B(5,8)$ $"endpoints A(1,2) and B(5,8)"$

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

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

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

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

$rArrB(5,8)toB'(8,-5)$

$color(blue)"Second transformation"$

$"under a dilatation of "((0),(-3))$

$• " a point "(x,y)to(x,y-3)$

$rArrA'(2,-1)toA''(2,-4)$

$rArrB'(8,-5)toB''(8,-8)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(-x,y)$

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

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

$"after all 3 transformations"$

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

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