Point A is at #(1 ,6 )# and point B is at #(5 ,-8 )#. Point A is rotated #pi # 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?

1 Answer
sankarankalyanam
Feb 6, 2018

New coordinates of #color(brown)(A (-6, -1)#

Reduction is distance due to rotation is #color(green)( ~~ 1.52# units

Explanation:

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A (1,6), B (5, -8)

From I to III quadrant

#A ((1),(6))-> A' ((-6), (-1))#

#bar(AB) = sqrt((1-5)^2 + (6-(-8))^2 = sqrt212#

#bar(A'B) = sqrt((-6-5)^2 + (-1+8)^2) = sqrt170#

Reduction is distance due to rotation is

#color(green)(sqrt212 - sqrt170 ~~ 1.52# units

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