Point A is at #(-7 ,7 )# and point B is at #(5 ,1 )#. 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?

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Answer 1 · 2018-02-07T01:58:15

New coordinates of A are #color(red)(7, -7)#

Change ( reduction ) in length of #vec(AB)# due to the rotation :

#color(green)(vec(AB) - vec(A'B) = 13.42 - 8.25 = 5.17)#

Given : A (-7, 7), B (5, 1). Rotated clockwise by #pi# about the origin.

Point A is in II quadrant and roated to IV quadrant

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#A((-7),(7)) -> A'((7),(-7)) #

New coordinates of A are #color(red)(7, -7)#

#vec(AB) = sqrt((-7-5)^2 + (7-1)^2) ~~ color(blue)(13.42)#

#vec(A'B) = sqrt((7-5)^2 + (-7-1)^2) ~~ color(blue)(8.25)#

Change (reduction) in length of #vec(AB)# due to the rotation :

#color(green)(vec(AB) - vec(A'B) = 13.42 - 8.25 = 5.17)#