Point A is at #(2 ,-3 )# and point B is at #(6 ,-6 )#. 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?

Question

1354 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-25T17:32:53

#(2, -3)-> (-2,3)# and #(6, -6)->(-6,6)#

No change in the distance.

The general rule is that in case of clockwise rotation by #pi#(or 180 degrees), # (x,y) -> (-x-y)#

Thus(2,-3 ) would become (-2, 3) and (6, -6) would become (-6,6)

The distance between A nd B =#sqrt((6-2)^2 +(-6+3)^2)=5#

After rotation the distance would be #sqrt((-6+2)^2 +(6-3)^2)=5#

This shows that there would be no change in the distance between the points after rotation.