Point A is at #(-5 ,9 )# and point B is at #(-6 ,7 )#. 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 · 2018-03-20T10:35:56

Increase in distance due to rotaion of point A about origin by #(3pi)/2# clockwise is

#color(brown)(vec(A'B) - vec(AB) = sqrt153 - sqrt5 = 10.13# units

# "Point" A (-5,9), B (-6,7)#

Point A rotated clockwise by #(3pi) / 2# about the origin.

Point A moves from II to III quadrant.

#A (-5,9) -> A'(-9,-5)#

Using distance formula,

#vec(AB) = sqrt((-5 +6)^2 + (9-7)^2) = sqrt5#

#vec(A'B) = sqrt((-9+6)^2 + (-5-7)^2) = sqrt153#

Increase in distance due to rotaion of point A about origin by #(3pi)/2# clockwise is

#vec(A'B) - vec(AB) = sqrt153 - sqrt5 = 10.13#