Question

Consider the diagram below. Point E is (-1,8) Point F is (5,-2). What is the distance of the line segment

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 8~) % (c,d) &&(~ 5 &,& -2~) \end{array}~~~ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[5-(-1)]^2+[-2-8]^2}\implies d=\sqrt{(5+1)^2+(-2-8)^2} \\\\\\ d=\sqrt{36+100}\implies d=\sqrt{136}\implies d=\sqrt{4\cdot 34} \\\\\\ d=\sqrt{2^2\cdot 34}\implies d=2\sqrt{34}$