In order to find this out we need to find the slopes of all those lines in question. Line XY, line YZ, and line XZ. If any 2 of those slopes are opposite reciprocals of each other, then those 2 lines are perpendicular and where perpendicular lines meet, a right angle is formed and this would, in fact, be a right triangle. So we need the slope formula to get the job done. The slope between X and Y first: [tex] m_{XY}=\frac{6-1}{5-1}=\frac{5}{4} [/tex]. The slope of line XY is 5/4. Now for the slope of line YZ: [tex] m_{YZ}=\frac{2-6}{6-5}=\frac{-4}{1}=-4 [/tex]. Finally we find the slope of line XZ: [tex] m_{XZ}=\frac{2-1}{6-1}=\frac{1}{5} [/tex]. None of the slopes are opposite reciprocals of each other so this is not a right triangle.
