A line segment has endpoints at $(9, 4)$ $(9 ,4 )$ and $(1, 8)$ $(1 , 8 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , 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 $(9, 4)$ $(9 ,4 )$ and $(1, 8)$ $(1 , 8 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-07-28T08:08:52

$(- 1, 9) and (3, 1)$ $(-1,9)" and "(3,1)$

Explanation:

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

$A = (9, 4) and B = (1, 8)$ $A=(9,4)" and "B=(1,8)$

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

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

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

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

$B(1,8)toB'(-8,1)$

$color(blue)"second transformation"$

$"under a horizontal translation "((5),(0))$

$• " a point "(x,y)to(x+5,y)$

$A'(-4,9)toA''(1,9)$

$B'(-8,1)toB''(-3,1)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$A''(1,9)toA'''(-1,9)$

$B''(-3,1)toB'''(3,1)$

$"After all 3 transformations"$

$(9,4)to(-1,9)" and "(1,8)to(3,1)$

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A line segment has endpoints at $(9, 4)$ $(9 ,4 )$ and $(1, 8)$ $(1 , 8 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , 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 (9 ,4 )(9,4)(9 ,4 ) and (1 , 8 )(1,8)(1 , 8 ). If the line segment is rotated about the origin by pi /2 π2 pi /2 , translated horizontally by 5 5 5 , 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 $(9, 4)$ $(9 ,4 )$ and $(1, 8)$ $(1 , 8 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?