Point A is at (-2 ,-8 ) and point B is at (-5 ,3 ). 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
Mar 12, 2016

Let Initial polar coordinate of A ,(r,theta)
Given Initial Cartesian coordinate of A ,(x_1=-2,y_1=-8)
So we can write
(x_1=-2=rcosthetaandy_1=-8=rsintheta)
After 3pi/2 clockwise rotation the new coordinate of A becomes
x_2=rcos(-3pi/2+theta)=rcos(3pi/2-theta)=-rsintheta=-(-8)=8

y_2=rsin(-3pi/2+theta)=-rsin(3pi/2-theta)=rcostheta=-2

Initial distance of A from B(-5,3)
d_1=sqrt(3^2+11^2)=sqrt130
final distance between new position of A(8,-2) and B(-5,3)
d_2=sqrt(13^2+5^2)=sqrt194
So Difference=sqrt194-sqrt130

also consult the link

http://socratic.org/questions/point-a-is-at-1-4-and-point-b-is-at-9-2-point-a-is-rotated-3pi-2-clockwise-about#238064