Point A is at #(6 ,2 )# and point B is at #(3 ,8 )#. Point A is rotated #(3pi)/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?

1 Answer
Shiva Prakash M V
Feb 7, 2018

(-2,6) is the new coordinate of Point A
Now, the points are closer by 1.323

Explanation:

Origin #(0,0)#
Point A#(6,2)#
Point B#(3,8)#

Distance between points A and B is
#sqrt((8-2)^2+(3-6)^2#
#=sqrt(6^2+3^2#
#=sqrt(36+9#
#=sqrt(45)#
#=6.708#

After transformation
Rotation by #(3pi)/2#
When rotated by#pi/2 #
the new coordinates are #(2,-6)#
When further rotated by #pi#
the coordinates are further transformed into #-2,6)#
#(-2,6)# is the transformed coordinate of the point A

After transformation
Point A#(-2,6)#
Point B#(3,8)#

Distance after transformation is
#sqrt((8-6)^2+(3-(-2))^2#
#=sqrt(2^2+5^2#
#=sqrt(4+25#
#=sqrt(29)#
#=5.385#

The distance between the points A and B has changed by
#5.385-6.708=-1.323#

Now, the points are closer by 1.323

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