Use slopes to determine if the triangle whose vertices are (-4,4) ​,(1,5) ​, and (2,0) is a right triangle.

Question

Find the slope for the side of the triangle between the vertices

(−4,4) and (1,5). m =

Answer 1

Sketching the point helps us understand where the right angle MIGHT be:

It appears to be at angle B as I have designated the vertices in the sketch.

If so, line AB would be perpendicular to line BC. To find out, calculate the slopes of each:

The slope equation is m = (y₂ - y₁)/(x₂ - x₁)

The slope of AB then = (5 - 4)/(1 - -4) = 1/5

The slope of BC then = (0 - 5)/(2 - 1) = -5/1

Since these slopes are negative reciprocals of each other, the lines are perpendicular. If the lines are perpendicular, angle B is a right angle. If angle B is a right angle, the triangle is a right triangle.