Question

The verticles of a triangle are A(1,2), B(3,4), and (4,1) What is the length of the shortest side

Answer 1

Check the picture below.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &A&(~ 1 &,& 2~) % (c,d) &B&(~ 3 &,& 4~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(3-1)^2+(4-2)^2}\implies AB=\sqrt{2^2+2^2} \\\\\\ AB=\sqrt{2\cdot 2^2}\implies AB=2\sqrt{2}$