A line segment has endpoints at $(2, 1)$ $(2 ,1 )$ and $(7, 3)$ $(7 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , 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 $(2, 1)$ $(2 ,1 )$ and $(7, 3)$ $(7 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-04-26T10:14:04

$(0, - 2) and (- 2, - 7)$ $(0,-2)" and "(-2,-7)$

Explanation:

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

$A (2, 1) and B (7, 3)$ $A(2,1)" and "B(7,3)$

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

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

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

$rArrA(2,1)toA'(-1,2)$

$rArrB(7,3)toB'(-3,7)$

$color(blue)"Second transformation"$

$"under a translation "((1),(0))$

$• " a point "(x,y)to(x+1,y)$

$rArrA'(-1,2)toA''(0,2)$

$rArrB'(-3,7)toB''(-2,7)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(x,-y)$

$rArrA''(0,2)toA'''(0,-2)$

$rArrB''(-2,7)toB'''(-2,-7)$

$"After all 3 transformations"$

$(2,1)to(0,-2)" and "(7,3)to(-2,-7)$

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A line segment has endpoints at $(2, 1)$ $(2 ,1 )$ and $(7, 3)$ $(7 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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Humanities

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A line segment has endpoints at (2 ,1 )(2,1)(2 ,1 ) and (7 , 3 )(7,3)(7 , 3 ). If the line segment is rotated about the origin by pi /2 π2 pi /2 , translated horizontally by 1 1 1 , 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 $(2, 1)$ $(2 ,1 )$ and $(7, 3)$ $(7 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the x-axis, what will the line segment's new endpoints be?