What is the distance between #(2, 8)# and #(5, 12)#?
If you use Euclidean distance, the distance is the square root of the sum of squares of (1) the difference in the x coordinates, i.e.
The shortest distance between points is a straight line, say A, connecting them. To determine the length consider a right triangle made out of two additional lines, say B, parallel to the X-axis connecting the points (2,8) and (5,8) and, say (C) connecting the points (5,8) and (5,12). Clearly, the distance of these two lines are 3 and 4, respectively. By the Pythagorean theorem, for a right triangle with sides B and C and A, we have