Question

Point A is at `(8 ,7 )` and point B is at `(-3 ,9 )`. 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 of Point `color(red)(A ((-7),(8))`

Change (reduction) in distance due to rotation between A - B is

`color(green)(11.18 - 4.12 = 7.06)`

Explanation:

A (8,7), B(-3,9). Rotated clockwise about origin by `(3pi)/2`

Distance `vec(AB) = sqrt((8+3)^2 + (7-9)^2) = sqrt125 ~~ color(blue(11.18)`

`A ((8),(7)) to A' ((-7),(8))` Moved from IV to I quadrant

Distance `vec(A'B) = sqrt((-7+3)^2 + (8-9)^2) = sqrt17 ~~ color(blue(4.12)`

Change (reduction) in distance due to rotation

`color(green)(11.18 - 4.12 = 7.06)`