Question

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

Answer 1

`(2, 5)` and `(4, 8)`

Explanation:

Rotation through `pi/2` about the origin maps `(a, b)` to `(-b, a)`

Vertical translation by `3` maps `(a, b)` to `(a, b+3)`

Reflection about the `y`-axis maps `(a, b)` to `(-a, b)`

Performing each of these in sequence:

`(a, b) -> (-b, a) -> (-b, a+3) -> (b, a+3)`

Hence:

`(2, 2) -> (2, 5)`

`(5, 4) -> (4, 8)`