Question

What is the length of the longest side of a triangle that has the vertices (-5, 6), (-5, -2), and (1, -2)?

Answer 1

Check the picture below.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& 6~) % (c,d) &&(~ 1 &,& -2~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1-6]^2+[-2-(-5)]^2}\implies d=\sqrt{(1-6)^2+(-2+5)^2} \\\\\\ d=\sqrt{(-5)^2+3^2}\implies d=\sqrt{25+9}\implies d=\sqrt{34}$