A line segment has endpoints at $(0, 0)$ $(0 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?

Question

A line segment has endpoints at $(0, 0)$ $(0 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Impact of this question

1587 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-22T14:01:17

$(- 5, 0) and (- 2, 1)$ $(-5,0)" and "(-2,1)$

Explanation:

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

$A (0, 0) and B (1, 3)$ $A(0,0)" and "B(1,3)$

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

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

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

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

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

$color(blue)"second transformation"$

$"under a translation "((5),(0))$

$• " a point "(x,y)to(x+5,y)$

$rArrA'(0,0)toA''(5,0)$

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

$color(blue)"third transformation"$

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

$• " a point "(x,y)to(-x,y)$

$rArrA''(5,0)toA'''(-5,0)$

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

$"after all 3 transformations"$

$(0,0)to(-5,0)" and "(1,3)to(-2,1)$

Science

Math

Humanities

... and beyond

A line segment has endpoints at $(0, 0)$ $(0 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , 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 (0 ,0 )(0,0)(0 ,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 5 5 5 , 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 $(0, 0)$ $(0 ,0 )$ and $(1, 3)$ $(1 , 3 )$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $pi /2$ , translated horizontally by $5$ $5$ , and reflected about the y-axis, what will the line segment's new endpoints be?