# Point A is at #(6 ,2 )# and point B is at #(3 ,-8 )#. 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

#### Explanation:

There is a formal method of doing this, and there is an easier way for simpler problems. I present the formal method first.

Given a point

Now, imagining you haven't taken trig yet (this is overkill for a 90 degree turn anyways), here's a (perhaps) more intuitive method.

Imagine taking the entire coordinate axis and rotating it 90 degrees clockwise about the origin in your head. The positive x-axis is now where the negative y-axis used to be. The positive y-axis is now where the positive x-axis used to be, and so on.

The point used to be at **down** and 2 units **right**. Make sure you can visualize this in your head, it's a useful skill. It might help to physically draw the coordinate axis, draw the point, and rotate the paper.

Down means negative y-axis, right means positive x-axis. The new coordinates for point

To determine how much the distance changed, we simply take the distances between