A line segment has endpoints at $(7, 3)$ $(7 ,3 )$ and $(6, 5)$ $(6 ,5)$ . 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 $(7, 3)$ $(7 ,3 )$ and $(6, 5)$ $(6 ,5)$ . 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 · 2018-03-23T20:48:45

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

Explanation:

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

$A (7, 3) and B (6, 5)$ $A(7,3)" and "B(6,5)$

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

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

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

$rArrA(7,3)toA'(3,-7)$

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

$color(blue)"Second transformation"$

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

$• " a point "(x,y)to(x,y+3)$

$rArrA'(3,-7)toA''(3,-4)$

$rArrB'(5,-6)toB''(5,-3)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$rArrA''(3,-4)toA'''(3,4)$

$rArrB'')5,-3)toB'''(5,3)$

$"After all 3 transformations"$

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

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A line segment has endpoints at $(7, 3)$ $(7 ,3 )$ and $(6, 5)$ $(6 ,5)$ . 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?

1 Answer

Explanation:

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A line segment has endpoints at (7 ,3 )(7,3)(7 ,3 ) and (6 ,5)(6,5)(6 ,5). 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 $(7, 3)$ $(7 ,3 )$ and $(6, 5)$ $(6 ,5)$ . 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?