If you imagine the two points on a grid, the difference between their x coordinates is 6 (9-3) and the distance between their y coordinates is 4 (|-2-2|).
In the Pythagorean theorem (a[tex] a^{2}+ b^{2} = c^{2} [/tex], these would count for the values of a and b, respectively (the legs of the triangle).
So, to find the hypotenuse, which is the distance between the points, square 6 and 4 to get 36 and 16, and find their sum: 52. 52, therefore, is the hypotenuse squared. So, find the square root of 52 to get [tex] \sqrt{52} [/tex], or ~7.2111 (exact form: [tex]2 \sqrt{13} [/tex])
From this is derived the distance formula,
[tex] \sqrt{ ( x_{2}- x_{1} )^{2}+ ( y_{2}- y_{1} )^{2} } [/tex]
