Point A is at #(-7 ,7 )# and point B is at #(5 ,-3 )#. 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?
1 Answer
Apr 5, 2016
A' = (7,-7) , d ≈ 10.85
Explanation:
Under a rotation of
#pi " about the origin "# a point A (x,y) → A' (-x,-y)
hence A (-7,7) → A' (7,-7)
To calculate the change in distance we will need to calculate the distance from A to B and also the distance from A' to B.
Using the
#color(blue)" distance formula " #
# d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) # where
#(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "# distance between A and B
here
#(x_1,y_1)=(-7,7)" and " (x_2,y_2)=(5,-3) # d
#=sqrt((5-(-7))^2+(-3-7)^2) = sqrt(144+100) ≈ 15.62# distance between A' and B
here
#(x_1,y_1)=(7,-7)" and " (x_2,y_2)=(5,-3)#
#d = sqrt((5-7)^2+(-3+7)^2) = sqrt(4+16) ≈ 4.77 # change in distance = 15.62 - 4.77 = 10.85
