A line segment has endpoints at $(7, 5)$ $(7 ,5 )$ and $(2, 6)$ $(2 ,6)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , 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 $(2, 6)$ $(2 ,6)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , 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 · 2018-01-06T14:51:50

$(- 5, - 10) and (- 6, - 5)$ $(-5,-10)" and "(-6,-5)$

Explanation:

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

$A (7, 5) and B (2, 6)$ $A(7,5)" and "B(2,6)$

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

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

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

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

$rArrB(2,6)toB'(-6,2)$

$color(blue)"second transformation"$

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

$• " a point "(x,y)to(x,y+3)$

$rArrA'(-5,7)toA''(-5,10)$

$rArrB'(-6,2)toB''(-6,5)$

$color(blue)"third transformation "$

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

$• " a point "(x,y)to(x,-y)$

$rArrA''(-5,10)toA'''(-5,-10)$

$rArrB''(-6,5)toB'''(-6,-5)$

$"under all 3 transformations"$

$(7,5)to(-5,-10)" and "(2,6)to(-6,-5)$

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