Point A is at #(9 ,3 )# and point B is at #(5 ,-6 )#. 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 · 2018-02-22T06:00:53

Decrease in distance due to rotation of point A is 6.2433

#A (9,3), B (5, -6)# A rotated clockwise by #(pi/2)# about origin.

#vec(AB) = sqrt((9-5)^2 + (3+6)^2) = sqrt97 = 9.8489#

#A’(x,y) = (3,-9)#

#vec(A’B) = sqrt ((3-5)^2 + (-9+6)^2) = sqrt13 = 3.6056#

Change in distance between #A’B, AB# is

#d = 3.6056 - 9.8489 = -6.2433#