Question

Point A is at `(4 ,-5 )` and point B is at `(-6 ,-2 )`. Point A is rotated `(3pi)/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

New coordinates `A’ (-5,-4)`

Change in distance `1.3849`, reduction.

Explanation:

Given `A (4, -5), B (-6,-2). Rotated about origin by`(3pi)/2#

To find A’ and `A’B - AB`

`vec(AB) = sqrt((4+6)^2 + (-5+2)^2) = sqrt109`

Coordinates of A’ (-5,-4)

`vec(A’B) = sqrt((-5-4)^2 + (-4+5)^2) = sqrt 82`

Change in distance `vec(AB) - vec(A’B) = sqrt109 - sqrt82 ~~ 1.3849`