If the slopes of two lines are opposite reciprocals of each other, then the lines are perpendicular. This means the angles formed are 90°. To prove this triangle is a right triangle, the opposite and adjacent side must have opposite reciprocal slopes.
Opposite Side:
[tex]m= \frac{y2-y1}{x2-x1} \\ \\ m= \frac{-3-1}{-2+5} \\ \\ m=- \frac{4}{3} [/tex]
Adjacent Side:
[tex]m= \frac{y2-y1}{x2-x1} \\ \\ m= \frac{-3-2}{-2-4} \\ \\ m= -\frac{5}{6} [/tex]
Since their slopes are not opposite reciprocals, we know that this is not a right triangle.
