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

1 Answer
Jan 8, 2016

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.


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)#.