# 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 Bhere

#(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 Bhere

#(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