A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(3, 8)$ $(3 ,8 )$ . 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 $(1, 2)$ $(1 ,2 )$ and $(3, 8)$ $(3 ,8 )$ . 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 · 2018-05-16T19:32:46

$(2, 2) and (8, 4)$ $(2,2)" and "(8,4)$

Explanation:

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

$A (1, 2) and B (3, 8)$ $A(1,2)" and "B(3,8)$

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

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

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

$rArrA(1.2)toA'(-2,1)$

$rArrB(3,8)toB'*-8,3)$

$color(blue)"Second transformation"$

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

$•" a point "(x,y)to(x,y+1)$

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

$rArrB'(-8,3)toB''(-8,4)$

$color(blue)"Third transformation"$

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

$• " a point "(x,y)to(-x,y)$

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

$rArrB''(-8,4)toB'''(8,4)$

$"After all 3 transformations"$

$(1,2)to(2,2)" and "(3,8)to(8,4)$

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A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(3, 8)$ $(3 ,8 )$ . 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 (1 ,2 )(1,2)(1 ,2 ) and (3 ,8 )(3,8)(3 ,8 ). 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 $(1, 2)$ $(1 ,2 )$ and $(3, 8)$ $(3 ,8 )$ . 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?