A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(9, 3)$ $(9 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?

Question

A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(9, 3)$ $(9 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?

2 Answers

Impact of this question

1571 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-19T02:02:46

$After all 3 transformations (1, 2) \to (4, 1) and (9, 3) \to (5, 9)$ $color(brown)("After all 3 transformations " color(orange)((1, 2)to(4, 1)" and "(9, 3)to(5, 9)$

Explanation:

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

$A (1, 2) and B (9, 3)$ $A(1, 2)" and "B(9, 3)$

$transformation of rotation about the origin of \frac{3 π}{2}$ $color(indigo)"transformation of rotation about the origin of "(3pi) / 2$

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

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

$rArrB(9, 3)toB'(3, -9)$

$color(indigo)"next transformation under a horizontal translation " ((2),(0))$

$• " a point "(x,y)to(x + 2, y)$

$rArrA'(2, -1) to A''(4, -1)$

$rArrB'(3, -9) to B''(5, -9)$

$color(indigo)"last transformation under a reflection in the x -axis"$

$• " a point "(x,y)to(x, -y)$

$rArrA''(4, -1)toA'''(4, 1)$

$rArrB''(5, -9)toB'''(5, 9)$

$color(brown)("After all 3 transformations " color(orange)((1, 2)to(4, 1)" and "(9, 3)to(5, 9)$

Answer 2 · 2018-07-19T07:56:14

$(4,1)" and "(5,9)$

Explanation:

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

$A=(1,2)" and "B=(9,3)$

$color(blue)"first transformation"$

$"under a rotation about the origin of "(3pi)/2$

$• " a point "(x,y)to(y,-x)$

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

$B(9,3)toB'(3,-9)$

$color(blue)"second transformation"$

$"under a horizontal translation "((2),(0))$

$• " a point "(x,y)to(x+2,y)$

$A'(2,-1)toA''(4,-1)$

$B'(3,-9)toB''(5,-9)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(x,-y)$

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

$B''(5,-9)toB'''(5,9)$

$"After all 3 transformations"$

$(1,2)to(4,1)" and "(9,3)to(5,9)$

Science

Math

Humanities

... and beyond

A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(9, 3)$ $(9 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A line segment has endpoints at (1 ,2 )(1,2)(1 ,2 ) and (9 ,3 )(9,3)(9 ,3 ). If the line segment is rotated about the origin by ( 3 pi)/2 3π2( 3 pi)/2 , translated horizontally by 2 2 2 , and reflected about the x-axis, what will the line segment's new endpoints be?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(9, 3)$ $(9 ,3 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $( 3 pi)/2$ , translated horizontally by $2$ $2$ , and reflected about the x-axis, what will the line segment's new endpoints be?