Question

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

Answer 1

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

Explanation:

We are going to use matrices.

The matrix of rotation of `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))`