Point A is at #(6 ,7 )# and point B is at #(-3 ,4 )#. 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?

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Answer 1 · 2018-02-22T07:20:10

There is a reduction in distance due to rotation of point A by #(3pi)/2# clockwise

#color(blue)(d = 9.4868 - 4.4721 = 5.0147#

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#A (6,7), B (-3,4)#. Point A Rotated clockwise by #(3pi)/2# about origin .

#A((6),(7)) -> A’ ((-7),(6))#

#vec(AB) = sqrt((6+3)^2 + (7-4)^2) = 9.4868#

# #vec(A’B) = sqrt((-7+3)^2 + (6-4)^2) = 4.4721#

There is a reduction in distance due to rotation of point A by #(3pi)/2# clockwise

#d = 9.4868 - 4.4721 = 5.0147#