Question

Point A is at `(8 ,4 )` and point B is at `(-3 ,1 )`. 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 A `(-4,8)`. There is no change in distance between AB & A’B.

Explanation:

Given : A (8,4), B (-3,1), A rotated by `(3pi)/2` clockwise about the origin.

To find A’, change in distance between A & B

Using distance formula,

`vec(AB) = sqrt((8+3)^2 + (4-1)^2) = sqrt130`

New coordinates of A `A’ ((4),(-8))`

`vec(A’B) = sqrt((4+3)^2 + (-8-1)^2) = sqrt(130`

There is no change in the distance between AB due to the rotation.