Point A is at #(-8 ,2 )# and point B is at #(7 ,-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?

1 Answer
sankarankalyanam
Feb 22, 2018

Decrease in distance due to the rotation by #pi#, #d =color(green)( 4.9985#

Explanation:

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#A (-8,2), B (7,-1)#

Rotated about the origin by #pi/2#, clockwise.

# vec(AB:) = sqrt((-8-7)^2 + (2+1)^2) = 15.2971#

#A ((-8),(2)) - > A’((2),(8))#

#vec(A’B) = sqrt((2-7)^2 + (8+1)^2) = 10.2956#

Decrease in distance due to the rotation by #pi#

#d = 15.2971 - 10.2956 = 4.9985#

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