Question

Point A is at `(-9 ,-4 )` and point B is at `(-5 ,-8 )`. 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

The new Point `A(4, -9)`
Difference `=d_n-d_o=sqrt82-4sqrt2=5.65685`

Explanation:

Original distance between point A and B
`d_o=sqrt((x_a-x_b)^2+(y_a-y_b)^2)`
`d_o=sqrt((-9--5)^2+(-4--8)^2)`
`d_o=sqrt((-4)^2+(4)^2)`
`d_o=4sqrt2`

the new distance `d_n`

Let `A(x_a, y_a)=(4, -9)`
`d_n=sqrt((x_a-x_b)^2+(y_a-y_b)^2)`

`d_n=sqrt((4--5)^2+(-9--8)^2)`
`d_n=sqrt((9)^2+(-1)^2)`
`d_n=sqrt(82)`

Difference `=d_n-d_o=sqrt82-4sqrt2=5.65685`

God bless....I hope the explanation is useful.