Point A is at #(-9 ,-1 )# and point B is at #(3 ,-4 )#. 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 clockwise rotation by #pi# is

#color(blue)(d = 4.5591#

Explanation:

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Given #A (-9,-1)#, #B(3,-4)#

Rotated about origin by #pi#, clockwise.

#vec(AB) = sqrt((-9-3)^2 + (-1+4)^2) = 12.3693#

#A((-9),(-1))-> A’((9),(1))#

#vec(A’B) = sqrt((9-3)^2 + (1+4)^2) = 7.8102#

Decrease in distance due to clockwise rotation by #pi# is

#d = 12.3693 - 7.8102 = 4.5591#

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