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 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