A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(6, 1)$ $(6 ,1)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi )/2$ , translated vertically by $3$ $3$ , 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 $(7, 5)$ $(7 ,5 )$ and $(6, 1)$ $(6 ,1)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi )/2$ , translated vertically by $3$ $3$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-02-03T20:53:42

$(5, 4) and (1, 3)$ $(5,4)" and "(1,3)$

Explanation:

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

$A (7, 5) and B (6, 1)$ $A(7,5)" and "B(6,1)$

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

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

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

$rArrA(7,5)toA'(5,-7)$

$rArrB(6,1)toB'(1,-6)$

$color(blue)"Second transformation"$

$"under a translation "((0),(3))$

$• " a point "(x,y)to(x,y+3)$

$rArrA'(5,-7)toA''(5,-4)$

$rArrB'(1,-6)toB''(1,-3)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

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

$rArrB''(1,-3)toB'''(1,3)$

$"after all 3 transformations"$

$(7,5)to(5,4)" and "6,1)to(1,3)$

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A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(6, 1)$ $(6 ,1)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi )/2$ , translated vertically by $3$ $3$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Explanation:

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A line segment has endpoints at (7 ,5 )(7,5)(7 ,5 ) and (6 ,1)(6,1)(6 ,1). If the line segment is rotated about the origin by (3pi )/2 3π2(3pi )/2 , translated vertically by 3 33 , 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 $(7, 5)$ $(7 ,5 )$ and $(6, 1)$ $(6 ,1)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi )/2$ , translated vertically by $3$ $3$ , and reflected about the x-axis, what will the line segment's new endpoints be?