Point A is at #(-8 ,-2 )# and point B is at #(7 ,-3 )#. 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 · 2018-02-14T07:12:16

Decrease in distance by rotating A to A’ is

#sqrt226 - sqrt202 ~~ color(purple)(0.82)#

#A ((-8),(-2)), B ((7),(-3))#

Point A rotated clockwise by #pi/2# about the origin.

Let A’ be the new point of A after rotation.

#A’((-2),(8))#. From third quadrant to second quadrant.

#vec(AB) = sqrt((-8-7)^2 + (-2+3)^2) = sqrt226#

#vec (A’B) = sqrt((-2-7)^2 + (8+3)^2) = sqrt202#

Decrease in distance by rotating A to A’ is

#sqrt226 - sqrt202 ~~ color(purple)(0.82)#