Question

The coordinates for the vertices of a right triangle are (1, 4), (6, 4), and (6,1). What is the length of the longer leg?

Answer 1

Check the picture below.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& 4~) % (c,d) &&(~ 6 &,& 1~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(6-1)^2+(1-4)^2}\implies d=\sqrt{5^2+(-3)^2} \\\\\\ d=\sqrt{25+9}\implies d=\sqrt{34}$