A line segment has endpoints at $(4, 2)$ $(4 ,2 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically by $1$ $1$ , 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 $(4, 2)$ $(4 ,2 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically by $1$ $1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-06-28T19:50:00

$(2, 5) and (1, 4)$ $(2,5)" and "(1,4)$

Explanation:

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

$A = (4, 2) and B = (3, 1)$ $A=(4,2)" and "B=(3,1)$

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

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

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

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

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

$color(blue)"second transformation"$

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

$• " a point "(x,y)to(x,y+1)$

$A'(-2,4)toA''(-2,5)$

$B'(-1,3)toB''(-1,4)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$A''(-2,5)toA'''(2,5)$

$B''(-1,4)toB'''(1,4)$

$"After all 3 transformations "$

$(4,2)to(2,5)" and "(3,1)to(1,4)$

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A line segment has endpoints at $(4, 2)$ $(4 ,2 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically by $1$ $1$ , 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 (4 ,2 )(4,2)(4 ,2 ) and (3 ,1 )(3,1)(3 ,1 ). If the line segment is rotated about the origin by pi /2 π2pi /2 , translated vertically by 1 11 , 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 $(4, 2)$ $(4 ,2 )$ and $(3, 1)$ $(3 ,1 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated vertically by $1$ $1$ , and reflected about the y-axis, what will the line segment's new endpoints be?