Point A is at (-7 ,4 ) and point B is at (2 ,-1 ). 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?

Feb 22, 2018

Due to rotation of A distance reduced between A and B by 4.4646

Explanation:

A((-7),(4)) -> A’((7),(-4))

$\vec{A B} = \sqrt{{\left(- 7 - 2\right)}^{2} + {\left(4 + 1\right)}^{2}} = 10.2956$

vec (A’B) = sqrt((7-2)^2 + (-4+1)^2) = 5.831

Distance change

vec(AB) - vec (A’B) = 10.2956 - 5.831 = 4.4646