Question

A line segment with endpoints at `(1, 5)` and `(1, -2)` is rotated clockwise by `pi/2`. What are the new endpoints of the line segment?

Answer 1

`(4.5,1.5)` and `(-2.5,1.5)`

Explanation:

`pi/2` is `90^o` so the new position of the line is at right-angles to the old position which was vertical (constant `x` value).

The length of the line is `5-(-2) = 7`. The point about which the line rotates is the midpoint of the line and is therefore `(1,(5-3.5)) = (1,1.5)`

Because the line is now horizontal the new end points are `((1+3.5),1.5)` and `((1-3.5),1.5)` which are `(4.5,1.5)` and `(-2.5,1.5)`