Point A is at #(6 ,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?

Question

1647 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-08T13:30:24

Distance has increased by #9.036#

When a point #(x,y)# is rotated clockwise about the origin, its new coordintes are #(y,-x)#.

Hence when #A(6,2)# is rotated clockwise about the origin, the new coordinates are #(2,-6)#

Originally distance between #(6,2)# and #(3,8)# was

#sqrt((3-6)^2+(8-2)^2)=sqrt(9+16)=sqrt25=5#

This changes to

#sqrt((3-2)^2+(8-(-6))^2)=sqrt(1+196)=sqrt197=14.036#

Hence, distance has increased by #14.036-5=9.036#