Point A is at #(-2 ,-5 )# and point B is at #(-3 ,1 )#. Point A is rotated #pi/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?

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Answer 1 · 2016-03-04T09:30:47

New point #A(x_(a2),y_(a2))=(-5, 2)#
Difference in distance#=sqrt37-sqrt5=3.8466#

The original distance
#d=sqrt((x_(a1)-x_b)^2+(y_(a1)-y_b)^2)#

#d=sqrt((-2--3)^2+(-5-1)^2)#

#d=sqrt((1^2+(-6)^2)#

#d=sqrt(37)#

The new distance:

#d=sqrt((x_(a2)-x_b)^2+(y_(a2)-y_b)^2)#

#d=sqrt((-5--3)^2+(2-1)^2)#

#d=sqrt(4+1)#

#d=sqrt5#

God bless....I hope the explanation is useful.