Point A is at #(4 ,2 )# and point B is at #(3 ,6 )#. 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

1776 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-15T10:00:35

Increase in distance due to the rotation of point A by #pi/2# around origin is #color(red)(= 5.9267#

#A ((4),(2)), B ((3),(6))#. A rotated around origin by #pi/2#

Using distance formula #vec(AB) = sqrt((4-3)^2 + (2-6)^2) ~~ 4.1231#

#A’ => ((2),(-4))# from first to fourth quadrant.

#vec(A’B) = sqrt((3-2)^2 + (-4-6)^2) ~~10.0498#

Increase in distance due to the rotation of point A by #pi/2# around origin is #color(red)(10.0498-4.1231 = 5.9267#