Question

Determine if triangle XYZ with coordinates X(1, 1), Y(5, 6), and Z(6, 2) is a right triangle. Use evidence to support your claim.

Answer 1

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:
`m_(XY)=(6-1)/(5-1)=(5)/(4)`. The slope of line XY is 5/4. Now for the slope of line YZ:
`m_(YZ)=(2-6)/(6-5)=(-4)/(1)=-4`. Finally we find the slope of line XZ:
`m_(XZ)=(2-1)/(6-1)=(1)/(5)`. None of the slopes are opposite reciprocals of each other so this is not a right triangle.