A line segment has endpoints at $(6, 5)$ $(6 ,5 )$ and $(5, 7)$ $(5 ,7)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically 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 $(6, 5)$ $(6 ,5 )$ and $(5, 7)$ $(5 ,7)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-07-02T20:54:53

$(- 5, - 8) and (- 7, - 7)$ $(-5,-8)" and "(-7,-7)$

Explanation:

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

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

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

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

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

$A(6,5)toA'(-5,6)$

$B(5,7)toB'(-7,5)$

$color(blue)"second transformation"$

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

$• " a point "(x,y)to(x,y+2)$

$A'(-5,6)toA''(-5,8)$

$B'(-7,5)toB''(-7,7)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$A''(-5,8)toA'''(-5,-8)$

$B''(-7,7)toB'''(-7,-7)$

$"After all 3 transformations"$

$(6,5)to(-5,-8)" and "(5,7)to(-7,-7)$

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A line segment has endpoints at $(6, 5)$ $(6 ,5 )$ and $(5, 7)$ $(5 ,7)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically 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 (6 ,5 )(6,5)(6 ,5 ) and (5 ,7)(5,7)(5 ,7). If the line segment is rotated about the origin by pi /2 π2pi /2 , translated vertically by 2 22 , 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 $(6, 5)$ $(6 ,5 )$ and $(5, 7)$ $(5 ,7)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?