Point A is at #(-7 ,4 )# and point B is at #(2 ,-1 )#. Point A is rotated #pi # 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 · 2018-02-22T06:50:05

Due to rotation of A distance reduced between A and B by 4.4646

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#A((-7),(4)) -> A’((7),(-4))#

# vec (AB) = sqrt((-7-2)^2 + (4+1)^2) = 10.2956#

#vec (A’B) = sqrt((7-2)^2 + (-4+1)^2) = 5.831#

Distance change

#vec(AB) - vec (A’B) = 10.2956 - 5.831 = 4.4646#