Point A is at #(8 ,4 )# and point B is at #(-3 ,1 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

1 Answer
Feb 16, 2018

New coordinates of A #(-4,8)#. There is no change in distance between AB & A’B.

Explanation:

Given : A (8,4), B (-3,1), A rotated by #(3pi)/2# clockwise about the origin.

To find A’, change in distance between A & B

Using distance formula,

#vec(AB) = sqrt((8+3)^2 + (4-1)^2) = sqrt130#

New coordinates of A #A’ ((4),(-8))#

#vec(A’B) = sqrt((4+3)^2 + (-8-1)^2) = sqrt(130#

There is no change in the distance between AB due to the rotation.