Point A is at #(1 ,-4 )# and point B is at #(-9 ,-8 )#. 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 · 2018-02-07T02:55:59

A moved from point #((1),(-4)) to ((4),(1))#

Distance between A & B changed by #~~ color(blue)(+15.81)#

A (1,-4), B (-9,-8). Point A rotated clockwise about the origin by #(3pi)/2# from IV quadrant to I quadrant

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#A((1),(-4)) -> A'((4),(1))#

Using distance formula #sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)#

#vec(AB) = sqrt((1+9)^2 + (-4+8)^2) = sqrt116 ~~ color(blue)(10.77)#

#vec(A'B) = sqrt((4+9)^2 + (1+8)^2) = sqrt250 ~~ color(blue)(15.81)#