A line segment has endpoints at $(5, 2)$ $(5 ,2 )$ and $(3, 4)$ $(3 ,4 )$ . If the line segment is rotated about the origin by $\frac{3 π}{2}$ $(3 pi)/2$ , translated vertically by $4$ $4$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2017-04-30T12:56:13

The new end points are $(- 2, - 5)$ $(-2,-5)$ and $(- 4, - 3)$ $(-4,-3)$

We are going to use matrices.

The matrix of rotation of $\frac{3}{2} π$ $3/2pi$ about the origin is

$((0,1),(-1,0))$

The matrix of reflection in the $y$ -axis is

$((-1,0),(0,1))$

The combination of the 2 operations is

$((-1,0),(0,1))*((0,1),(-1,0))=((0,-1),(-1,0))$

The new end points are

$((0,-1),(-1,0))((5),(2))=((-2),(-5))$

and

$((0,-1),(-1,0))*((3),(4))=((-4),(-3))$

A line segment has endpoints at (5 ,2 )(5,2)(5 ,2 ) and (3 ,4 )(3,4)(3 ,4 ). If the line segment is rotated about the origin by (3 pi)/2 3π2(3 pi)/2 , translated vertically by 4 44 , and reflected about the y-axis, what will the line segment's new endpoints be?