Question

A line segment with endpoints at `(3 , -2 )` and `(5, 8 )` is rotated clockwise by `(3 pi)/2`. What are the new endpoints of the line segment?

Answer 1

( 3,-2) would change to (2,3)
and (5,8) would change to (-8,5)

Explanation:

To find the new coordinates, the process of clockwise rotation by `(3pi)/2`can be split in two parts:
I. First rotate by `pi/2` in which (x,y) `->` (y,-x)

II Next rotate by `pi` in which (x,y) `->` (-x,-y)

Thus any point (x,y) on rotation by `(3pi)/2` would become (-y,x)

Thus ( 3,-2) would change to (2,3)
and (5,8) would change to (-8,5)