Point A is at #(5 ,3 )# and point B is at #(-3 ,2 )#. 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

Point A is at #(5 ,3  )# and point B is at #(-3  ,2   )#.  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?

James Atkins · Accepted Answer

#color(purple)(1.16 " is the change in the distance between A & B"# #color(orange)("due to the rotation of A by " (pi)/2 " clockwise about the origin"#

#A (5,3), B (-3, 2), " A rotated "pi/2 " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((5+3)^2 + (3-2)^2) ~~ 8.06#

#A (5,3) to A'(3,-5), " as per rotation rule"#

#bar (A'B) = sqrt((3+3)^2 + (-5-2)^2) ~~ 9.22#

#"Change in distance "= 9.22 - 8.06 = 1.16#

#color(purple)(1.16 " is the change in the distance between A & B"# #color(orange)("due to the rotation of A by " (pi)/2 " clockwise about the origin"#

Carson Arnold · Answer

undefined The new coordinates of point A after rotating $ \pi/2 $ clockwise about the origin are (-3, 5). The distance between the new coordinates of point A and point B is the same as the distance between the original points A and B because rotating a point about the origin does not change its distance from other points. Therefore, the distance between points A and B remains unchanged.