Question

How to find the distance between (3,-2) and (9,2) using pythagorean theorum?

Answer 1

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$a^{2}+ b^{2} = c^{2}$, 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 $\sqrt{52}$, or ~7.2111 (exact form: $2 \sqrt{13}$)

From this is derived the distance formula, 
$\sqrt{ ( x_{2}- x_{1} )^{2}+ ( y_{2}- y_{1} )^{2} }$