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

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Answer 1 · 2018-07-31T10:31:12

$(9, 4) and (10, 2)$ $(9,4)" and "(10,2)$

Explanation:

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

$A = (4, 2) and B = (2, 3)$ $A=(4,2)" and "B=(2,3)$

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

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

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

$A(4,2)toA'(2,-4)$

$B(2,3)toB'(3,-2)$

$color(blue)"second transformation"$

$"under a horizontal translation "((7),(0))$

$• " a point "(x,y)to(x+7,y)$

$A'(2,-4)toA''(9,-4)$

$B'(3,-2)toB''(10,-2)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$A''(9,-4)toA'''(9,4)$

$B''(10,-2)toB'''(10,2)$

$"After all 3 transformations"$

$(4,2)to(9,4)" and "(2,3)to(10,2)$

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A line segment has endpoints at $(4, 2)$ $(4 , 2)$ and $(2, 3)$ $(2 ,3)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $7$ $7$ , 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 (4 , 2)(4,2)(4 , 2) and (2 ,3)(2,3)(2 ,3). If the line segment is rotated about the origin by (3pi)/2 3π2(3pi)/2 , translated horizontally by 777, 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 $(4, 2)$ $(4 , 2)$ and $(2, 3)$ $(2 ,3)$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3pi)/2$ , translated horizontally by $7$ $7$ , and reflected about the x-axis, what will the line segment's new endpoints be?