Point A is at #(8 ,7 )# and point B is at #(-3 ,9 )#. 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 · 2018-02-07T03:18:58

New coordinates of Point #color(red)(A ((-7),(8))#

Change (reduction) in distance due to rotation between A - B is

#color(green)(11.18 - 4.12 = 7.06)#

A (8,7), B(-3,9). Rotated clockwise about origin by #(3pi)/2#

Distance #vec(AB) = sqrt((8+3)^2 + (7-9)^2) = sqrt125 ~~ color(blue(11.18)#

#A ((8),(7)) to A' ((-7),(8))# Moved from IV to I quadrant

Distance #vec(A'B) = sqrt((-7+3)^2 + (8-9)^2) = sqrt17 ~~ color(blue(4.12)#

Change (reduction) in distance due to rotation

#color(green)(11.18 - 4.12 = 7.06)#