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

Question

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

1 Answer

Impact of this question

1602 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-27T07:16:48

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

Explanation:

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

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

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

$under a rotation about the origin of \frac{3 π}{2}$ $"under a rotation about the origin of "(3pi)/2$

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

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

$B(2,2)toB'(2,-2)$

$color(blue)"second transformation"$

$"under a vertical translation "((0),(-3))$

$• " a point "(x,y)to(x,y-3)$

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

$B'(2,-2)toB''(2,-5)$

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

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

$B''(2,-5)toB'''(-2,-5)$

$"After all 3 transformations"$

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

Science

Math

Humanities

... and beyond

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

1 Answer

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 (2 , 2 )(2,2)(2 , 2 ). If the line segment is rotated about the origin by (3 pi ) /2 3π2(3 pi ) /2 , translated vertically by -3 −3 -3 , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

Related questions

Impact of this question

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