Question

Point A is at `(6 ,2 )` and point B is at `(3 ,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

(-2,6) is the new coordinate of Point A
Now, the points are closer by 1.323

Explanation:

Origin `(0,0)`
Point A`(6,2)`
Point B`(3,8)`

Distance between points A and B is
`sqrt((8-2)^2+(3-6)^2`
`=sqrt(6^2+3^2`
`=sqrt(36+9`
`=sqrt(45)`
`=6.708`

After transformation
Rotation by `(3pi)/2`
When rotated by`pi/2`
the new coordinates are `(2,-6)`
When further rotated by `pi`
the coordinates are further transformed into `-2,6)`
`(-2,6)` is the transformed coordinate of the point A

After transformation
Point A`(-2,6)`
Point B`(3,8)`

Distance after transformation is
`sqrt((8-6)^2+(3-(-2))^2`
`=sqrt(2^2+5^2`
`=sqrt(4+25`
`=sqrt(29)`
`=5.385`

The distance between the points A and B has changed by
`5.385-6.708=-1.323`

Now, the points are closer by 1.323