Point A is at #(-5 ,9 )# and point B is at #(-1 ,4 )#. 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 · 2018-02-06T12:01:45

New coordinates of #color(brown)(A (-9, -5)#

Increase in distance caused by the rotation is

#color(green)(sqrt145 - sqrt41 ~~ 10.2# units

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#A (-5,9), B (-1,4)#

Point A is in II quadrant and moves to III quadrant where both x & y are negative.

#vec(AB) = ((-5),(9)) -> vec(A'B) = ((-9),(-5))#

By distance formula,

#vec(AB) = sqrt((-5+1)^2 + (9-4)^2) = sqrt41#

#vec(A'B) = sqrt((-9+1)^2 + (-5-4)^2) = sqrt145#

Increase in distance caused by the rotation is

#color(green)(sqrt145 - sqrt41 ~~ 10.2# units