The line from the point (5,5) to (5,1) has length 4
units. We can just subtract 5 1= 4 or in other word (y_{2}y_{1}) 
The line from the point (2,1) to (5,1) has length 4
units. We can just subtract 5  2 = 3 or in other word (x_{2}x_{1}) 
By the theorem pythagoras we know that the hypoteneuse^{2}=sum of squares of other two sides. (Pythagoras theorem examples) 

In the diagram we can see that one of the sides is the difference in the height of the point =y_{2}y_{1 }The other side is the difference in the distance across =x_{2}x_{1}  
So the side or the hypoteneuse is equal to the sum of the squares of the other 2 sides  
hyp^{2} = (x_{2}x_{1})^{2 }+ (y_{2}y_{1})^{2}  
Therefore if we get the square root of both sides we get the distance formula.  


Exercise 