SOLUTION: Find the image of point (5,3) when it is rotated 1/4 turn counter-clockwise around the point (1,-4)

     

You can tell the answer is (-6,0).  

To rotate 90 counter-clockwise about a center point, 
1. count the number of horizontal and vertical units it is from the 
   center point to the original point.   
2. The image point will be the same number of units horizontal from
   the center point as the original point is vertical from the center 
   point.
3. The image point will be the same number of units vertical from
   the center point as the original point is horizontal from the center 
   point.  
4. There are rules about going right, left, up, or down, but it's
   easier just to use common sense.

To get from the center point to the original point, we had to go right 4
units and up 7 units.  Therefore to get from the center point to the
image point we had to go left 7 units and up 4 units.  The "left" and
"up" we got from common sense, because if you went any other way it 
would not look like a rotation of 90o.

Edwin