# 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. ${\left(5 - 2\right)}^{2}$ or 9 and (2) the difference in the y coordinates, i.e. ${\left(12 - 8\right)}^{2}$ or 16. Since 25 = $16 + 9$, the square root of that, namely 5, is the answer.
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 ${A}^{2} = {B}^{2} + {C}^{2}$, or, equivalently, by taking square roots of both sides of this equation, A = $\sqrt{{B}^{2} + {C}^{2}}$.