A line segment has endpoints at $(7, 4)$ $(7 ,4 )$ and $(2, 6)$ $(2 ,6)$ . 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 $(7, 4)$ $(7 ,4 )$ and $(2, 6)$ $(2 ,6)$ . 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 · 2018-02-02T21:26:23

$(4, 4) and (6, - 1)$ $(4,4)" and "(6,-1)$

Explanation:

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

$A (7, 4) and B (2, 6)$ $A(7,4)" and "B(2,6)$

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

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

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

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

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

$color(blue)"Second transformation"$

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

$• " a point "(x,y)to(x,y+3)$

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

$rArrB'(6,-2)toB''(6,1)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

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

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

$"after all 3 transformations"$

$(7,4)to(4,4)" and "(2,6)to(6,-1)$

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A line segment has endpoints at $(7, 4)$ $(7 ,4 )$ and $(2, 6)$ $(2 ,6)$ . 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 ,4 )(7,4)(7 ,4 ) and (2 ,6)(2,6)(2 ,6). 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 $(7, 4)$ $(7 ,4 )$ and $(2, 6)$ $(2 ,6)$ . 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?