# Point A is at #(4 ,-2 )# and point B is at #(1 ,-3 )#. Point A is rotated #pi/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?

##### 1 Answer

The new point

and No change in distance. Same distance

#### Explanation:

the equation passing thru the origin (0, 0) and point A(4, -2) is

and distance from (0, 0) to A(4, -2) is

the equation passing thru the origin (0, 0) and perpendicular to line

We are looking for a new point

Use distance formula for "distance from line to a point not on the line"

Use equation,

Using first and second equation. Solve for

and