A line segment has endpoints at $(7, 4)$ $(7 ,4 )$ and $(5, 9)$ $(5 ,9)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $5$ $5$ , 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 $(5, 9)$ $(5 ,9)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2017-06-07T19:13:24

$(- 4, - 2) and (- 9, 0)$ $(-4,-2)" and " (-9,0)$

Explanation:

Since there are 3 transformations to be performed, label the endpoints.
$A (7, 4) and B (5, 9)$ $A(7,4)" and " B(5,9)$

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

$Under a rotation about the origin of \frac{π}{2}$ $"Under a rotation about the origin of " pi/2$

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

$rArrA(7,4)toA'(-4,7)" and " B(5,9)toB'(-9,5)$

$color(blue)"Second transformation"$

$"Under a translation of " ((0),(-5))$

$"a point " (x,y)to(x,y-5)$

$rArrA'(-4,7)toA''(-4,2)$

$"and " B'(-9,5)toB''(-9,0)$

$color(blue)"Third transformation"$

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

$"a point " (x,y)to(x,-y)$

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

$"and " B''(-9,0)toB'''(-9,0)$

$"After all 3 transformations"$

$(7,4)to(-4,-2)" and " (5,9)to(-9,0)$

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A line segment has endpoints at $(7, 4)$ $(7 ,4 )$ and $(5, 9)$ $(5 ,9)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $5$ $5$ , 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 (5 ,9)(5,9)(5 ,9). If the line segment is rotated about the origin by (pi )/2 π2(pi )/2 , translated vertically by 5 55 , 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 $(5, 9)$ $(5 ,9)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?