Point A is at #(4 ,1 )# and point B is at #(-6 ,-7 )#. 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
Leland Adriano Alejandro
Feb 16, 2016

The new point A is at #(-1, 4)#
The changed in distance between points A and B
#=2sqrt41-sqrt(146)=0.723203#

Explanation:

Rotating point A (4, 1) about the origin by #(3pi)/2# clockwise will place it exactly at (-1, 4) at the 2nd quadrant. The new distance between A and B is #=sqrt146#. The distance between point B(-6, -7) and the original location of point A(4, 1) is #=sqrt(164)=2sqrt(41)#

difference in distance#=sqrt(164)-sqrt(146)=0.723203#

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