Dear Louis,

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

d = √((x₁ - x₂)² + (y₁ - y₂)²)  
 ( -2 , 5 )   ( 12 , -1 )  
   ↑    ↑         ↑     ↑      
  x₁    y₁        x₂    y₂  

d = √((-2 - 12)² + (5 - (-1))²) = √((-14)² + 6²) = √(196 + 36) = √232 = 2√58 ≈ 15.23

The distance between two  points (x_1,y_{1) and} (X_2,Y_{2) can be found by using the formula d =  √ (}x_{2-X1)²+(Y2-y1)²}

you can find the distance for the points (-2,5) and (12,-1) using the above formula