coordinate geometry

Create point c(2,2) in order to form a triangle.

Now you have 3 sides of the triangle

side ac (length 1)
side bc ( length 1)
and side ab (length ?)

Use pythagorean theorem which says the length of the hypotenuse of a right angled triangle is the squareroot of the sum of the squares of the other 2 sides.

square of side ac is 1^2 = 1
square of side bc is 1^2 = 1
length of ab = sqrt(1 + 1) = sqrt(2)

d=sqrt[(x2-x1)^2 +(y2-y1)^2]
=sqrt[1^2 +1^2]
=sqrt[2}
=1.414

You don't need a triangle. This theorem is extendable to n dimensions.