Point A is at #(1 ,-1 )# and point B is at #(-2 ,1 )#. 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 · 2018-02-07T02:47:13

New coordinates of #color(red)(A ((1),(1))#

Change (reduction) in distance from #bar(AB), bar(A'B)# is

#=> sqrt13 - 3 ~~ color(green)(0.61)#

A (1, -1), B (-2,1) and rotated by #(3pi)/2# clockwise about the origin.

Point A moves from IV quadrant to I quadrant.

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

Distance #vec(AB) = sqrt((1+2)^2 + (-1-1)^2) = color(blue)(sqrt13#

Distance #vec(A'B) = sqrt((1+2)^2 + (1-1)^2) = color(blue)3#

Change (reduction) in distance from #bar(AB), bar(A'B)# is

#=> sqrt13 - 3 ~~ color(green)(0.61)#