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

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Answer 1 · 2016-09-10T22:00:12

The new A is #(2,-3)# and the difference in the distance is approximately #4.9#.

A #pi/2# or #90# degrees clockwise rotation of a point can be written as #(x,y)->(y,-x)#.

So, #(3,2)# rotated #pi/2# clockwise becomes #(2,-3)#.

The distance between the original point A (3,2) and B (3,-8) can be found using the distance formula.

#sqrt((3-3)^2+(-8-2)^2##= sqrt((-10)^2)##=sqrt100##=10#

The distance between the new point A (2,-3) and B (3,-8) is

#sqrt((3-2)^2+(-8- -3)^2)##=sqrt(1^2+(-5)^2)##=sqrt(1+25)##=sqrt26##~=5.1#

The difference between the A and B changes by approximately #10-5.1 = 4.9#