If I have two points, (-2, -3) and (-4, 4) then the distance between them is sqrt(53)
What geometric proof defines this?
Plot the points $\displaystyle (-4,4),~(-4,-3)~\&~(-2,-3)$.
Draw that triangle.You will have a nice right triangle.
The length of hypotenuse is the distance we want.
The two legs have lengths 7 & 2.