Point A is at #(2 ,-6 )# and point B is at #(-8 ,-3 )#. 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 · 2018-02-06T10:21:08

New coordinate of #color(red)(A (-5, -2)#

Distance changed (increase) between A & B by #(pi/2)# clockwise rotation of A about the origin is #color(green)(sqrt109 - sqrt10 ~~ 7.28)#

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A (2, -6), B(-8, -3)

Point A rotated clockwise about the origin by #pi/2#

That means A changes from fourth quadrant to third quadrant.

Both x & y are negative.That means, x -> -y and y -> x.

#A ((2),(-5)) -> A'((-5),(-2))#

#AB = sqrt((2-(-8))^2 + (-6 - (-3))^2) = sqrt109#

#A'B = sqrt((-5-(-8))^2 + (-2 - (-3))^2) = sqrt10#

Distance changed between A & B by th#pi/2) clockwise rotation of A about the origin is

#A'B - AB = color(green)(sqrt109 - sqrt10 ~~ 7.28)#