A line segment has endpoints at $(7, 4)$ $(7 , 4)$ and $(2, 5)$ $(2 , 5)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 3$ $-3$ , 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 $(2, 5)$ $(2 , 5)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 3$ $-3$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-07-19T08:17:33

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

Explanation:

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

$A = (7, 4) and B = (2, 5)$ $A=(7,4)" and "B=(2,5)$

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

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

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

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

$B(2,5)toB'(5,-2)$

$color(blue)"second transformation"$

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

$• " a point "(x,y)to(x-3,y)$

$A'(4,-7)toA''(1,-7)$

$B'(5,-2)toB''(2,-2)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$A''(1,-7)toA'''(-1,-7)$

$B''(2,-2)toB'''(-2,-2)$

$"After all 3 transformations"$

$(7,4)to(-1,-7)" and "(2,5)to(-2,-2)$

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A line segment has endpoints at $(7, 4)$ $(7 , 4)$ and $(2, 5)$ $(2 , 5)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 3$ $-3$ , 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 (2 , 5)(2,5)(2 , 5). If the line segment is rotated about the origin by (3pi)/2 3π2(3pi)/2 , translated horizontally by -3−3-3, 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 $(2, 5)$ $(2 , 5)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $- 3$ $-3$ , and reflected about the y-axis, what will the line segment's new endpoints be?