A line segment has endpoints at $(2, 0)$ $(2 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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A line segment has endpoints at $(2, 0)$ $(2 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-03-14T11:12:18

$(- 1, 2) and (2, 1)$ $(-1,2)" and "(2,1)$

Explanation:

$since there are 3 transformations to be performed$ $"Since there are 3 transformations to be performed"$

$Label the endpoints A (2, 0) and B (1, 3)$ $"Label the endpoints "A(2,0)" and "B(1,3)$

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

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

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

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

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

$color(blue)"second transformation"$

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

$• " a point "(x,y)to(x+1,y)$

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

$rArrB'(-3,1)toB''(-2,1)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

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

$rArrB''(-2,1)toB'''(2,1)$

$"After all 3 transformations"$

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

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A line segment has endpoints at $(2, 0)$ $(2 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at (2 ,0 )(2,0)(2 ,0 ) and (1 , 3 )(1,3)(1 , 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 y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at $(2, 0)$ $(2 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $1$ $1$ , and reflected about the y-axis, what will the line segment's new endpoints be?