A line segment has endpoints at $(7, 4)$ $(7 ,4 )$ and $(8, 5)$ $(8 ,5 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi)/2$ , translated vertically by $- 2$ $-2$ , 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 $(7, 4)$ $(7 ,4 )$ and $(8, 5)$ $(8 ,5 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi)/2$ , translated vertically by $- 2$ $-2$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-02-23T14:03:41

$(- 4, - 9) and (- 5, - 10)$ $(-4,-9)" and "(-5,-10)$

Explanation:

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

$A (7, 4) and B (8, 5)$ $A(7,4)" and "B(8,5)$

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

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

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

$rArrA(7,4)toA'(4,-7)$

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

$color(blue)"Second transformation"$

$"under a translation "((0),(-2))$

$• " a point "(x,y)to(x,y-2)$

$rArrA'(4,-7)toA''(4,-9)$

$rArrB'(5,-8)toB''(5,-10)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$rArrA''(4,-9)toA'''(-4,-9)$

$rArrB''(5,-10)toB'''(-5,-10)$

$"After all 3 transformations"$

$(7,4)to(-4,-9)" and "(8,5)to(-5,-10)$

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A line segment has endpoints at $(7, 4)$ $(7 ,4 )$ and $(8, 5)$ $(8 ,5 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi)/2$ , translated vertically by $- 2$ $-2$ , 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 ,4 )(7,4)(7 ,4 ) and (8 ,5 )(8,5)(8 ,5 ). If the line segment is rotated about the origin by (3 pi)/2 3π2(3 pi)/2 , translated vertically by -2 −2-2 , 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 $(7, 4)$ $(7 ,4 )$ and $(8, 5)$ $(8 ,5 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi)/2$ , translated vertically by $- 2$ $-2$ , and reflected about the y-axis, what will the line segment's new endpoints be?