Point A is at #(3 ,2 )# and point B is at #(-7 ,3 )#. 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?

1 Answer
David G.
Mar 21, 2016

Rotating Point A #(3, 2)# clockwise through #pi/2# yields Point A' #(2, -3)#. We can then calculate the distance between Point A' and Point B as approximately #10.8# #units#.

Explanation:

Now, #pi/2# is #1/4# of a full rotation (#2pi#) or #90^o#. If we rotate the point #(3, 2)# through this angle clockwise, we move from the first to the fourth quadrant, so the #x# value will still be positive and the #y# value will be negative.

You should probably draw a diagram, but it turns out that the new point, which we can call Point A', has the coordinates #(2, -3)#.

We can calculate the distance between Point A' and Point B:

#r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt(((-7)-2)^2+(3-(-3))^2)=sqrt(81+36)~~10.8#

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