Question

What is the distance between `(2, 8)` and `(5, 12)`?

Answer 1

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. `(5-2)^2` or 9 and (2) the difference in the y coordinates, i.e. `(12-8)^2` or 16. Since 25 = `16 +9`, the square root of that, namely 5, is the answer.

Explanation:

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)`.