Question

Find in simplest radical form, the length of the line segment joining points (1,5) and (3,9)

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& 5~) % (c,d) &&(~ 3 &,& 9~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(3-1)^2+(9-5)^2}\implies d=\sqrt{2^2+4^2}\implies d=\sqrt{20} \\\\\\ d=\sqrt{4\cdot 5}\implies d=\sqrt{2^2\cdot 5}\implies d=2\sqrt{5}$