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
P dilip_k
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

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