A line segment has endpoints at $(3, 4)$ $(3 , 4)$ and $(1, 9)$ $(1 ,9)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 2$ $-2$ , 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 $(3, 4)$ $(3 , 4)$ and $(1, 9)$ $(1 ,9)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 2$ $-2$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-04-18T11:15:25

$(- 2, 3) and (7, 1)$ $(-2,3)" and "(7,1)$

Explanation:

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

$A (3, 4) and B (1, 9)$ $A(3,4)" and "B(1,9)$

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

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

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

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

$rArrB(1,9)toB'(9,-1)$

$color(blue)"Second transformation"$

$"under a translation "((-2),(0))$

$• " a point "(x,y)to(x-2,y)$

$rArrA'(4,-3)toA''(2,-3)$

$rArrB'(9,-1)toB''(7,-1)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$rArrA''(2,-3)toA'''(2,3)$

$rArrB''(7,-1)toB'''(7,1)$

$"After all 3 transformations"$

$(3,4)to(2,3)" and "(1,9)to(7,1)$

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A line segment has endpoints at $(3, 4)$ $(3 , 4)$ and $(1, 9)$ $(1 ,9)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 2$ $-2$ , 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 (3 , 4)(3,4)(3 , 4) and (1 ,9)(1,9)(1 ,9). If the line segment is rotated about the origin by (3pi)/2 3π2(3pi)/2 , translated horizontally by -2−2-2, 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 $(3, 4)$ $(3 , 4)$ and $(1, 9)$ $(1 ,9)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 2$ $-2$ , and reflected about the x-axis, what will the line segment's new endpoints be?