Point A is at #(2 ,-4 )# and point B is at #(1 ,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 22, 2018

Decrease in distance due to rotation of point A about origin is

7.0416

Explanation:

Given : #A (2, -4), B (1,8)# Point A rotated clockwise about origin by #pi#.

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#A’(2,-4) -> A’ (-2, 4)# From IV quadrant to II.

#vec(AB) = sqrt((2-1)^2 + (-4-8)^2) = sqrt145 = 12.0416#

#vec(A’B) = sqrt((-2-1)^2 + (4-8)^2) = 5#

Change is distance

#vec (A’B) - vec(AB) = 5 - 12.0416 = - -7.0416#

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