Point A is at #(-8 ,2 )# and point B is at #(2 ,-1 )#. 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 · 2018-02-06T12:24:33

New coordinates of #A' color(blue)(((2), (8))#

Reduction in distance due rotation of A by #pi/2# clockwise is

#color(green)(= sqrt109 - 9 ~~ 1.44#

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A (-8, 2), B (2, -1)

Rotation of A #(pi/2)# clockwise about origin

A moves from II to I quadrant.

New coordinates of A

#A ((-8),(2)) -> A' color(blue)(((2), (8))#

#bar(AB) = sqrt((-8-2)^2 + (2-(-1))^2) = color(brown)(sqrt109#

#bar(A'B) = sqrt((2-2)^2 + (8-(-1))^2) = color(brown)(9#

Reduction in distance due rotation of A by #pi/2# clockwise is

#color(green)(= sqrt109 - 9 ~~ 1.44#