Point A is at #(1 ,3 )# and point B is at #(-1 ,2 )#. 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
Mar 20, 2018

Increase in distance due to rotation of coordinates of A about origin by #pi/2# clockwise is

#vec(AB) - vec(A’B) = color(red)(2.7639#

Explanation:

#vec (AB) = sqrt ((1+1)^2 + (3-2)^2) = sqrt5#

www.math-only-math.com/signs-of-coordinates.html

#A((1),(3)) -> A’ ((3),(-1))#

#vec(A’B) = sqrt((3+1)^2 + (-1-2)^2) = sqrt25 = 5#

Increase in distance due to rotation of coordinates of A

#vec(A'B) - vec(AB) = 5- sqrt5 = color(red)(2.7639#

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