Question

Determine whether the figure is a right triangle. a right triangle contains one 90 degree angle. Justify your answer with slopes. ( question 16)

Answer 1

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:

`m= (y2-y1)/(x2-x1) \\ \\ m= (-3-1)/(-2+5) \\ \\ m=- (4)/(3)`

Adjacent Side:

`m= (y2-y1)/(x2-x1) \\ \\ m= (-3-2)/(-2-4) \\ \\ m= -(5)/(6)`

Since their slopes are not opposite reciprocals, we know that this is not a right triangle.