finding the distance
You can figure out the precise distance between these two points by using what you know about right triangles: that the sum of the squares of the legs equals the square of the hypotenuse.
Here's how. First, plot both of these points (-2, 5) and (12, -1) on a piece of graph paper. Then what I want you to do is draw two lines: the first is a horizontal line going from (-2,5) to (12, 5). Then, turning the pencil in a different direction, draw a vertical line that goes from (12, 5) to (12, -1).
Voila. You have a right triangle and you will notice the length of the hypotenuse of this triangle is precisely equal to the length between these two points. If you count the tick-marks, you'll notice the legs of this right triangle have lengths 14 and 6. 14 squared plus 6 squared is equal to 232. The answer is, therefore, that the length is the SQUARE ROOT OF 232 or about 15.23.
The quick method is to think the DIFFERENCE in X is one leg of the triangle and the DIFFERENCE in Y is the other leg of your triangle. The difference between (-2) and 12 is 14. The difference between 5 and -1 is 6. Etc.
Mr. Gets Results