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?

1 Answer
bp
Nov 20, 2016

( 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)/2can 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)

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