Question

Point A is at `(6 ,-8 )` and point B is at `(-3 ,8 )`. 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?

Answer 1

Decrease in distance due to rotation of coordinates of A

`vec(AB) - vec(A’B) = color(red)(3.4915`

Explanation:

`vec (AB) = sqrt ((6+3)^2 + (-8-8)^2) = 18.3576`

`A((6),(-8)) -> A’ ((-8),(-6))`

`vec(A’B) = sqrt((-8+3)^2 + (-6-8)^2) = 14.8661`

Decrease in distance due to rotation of coordinates of A

`vec(AB) - vec(A’B) = 18.3576 - 14.8661 = color(red)(3.4915`