Question

How would you figure out if a triangle with vertices (0,5), (1,2.5), and (-10,1) is a right triangle?

Answer 1

Prove right triangle

Explanation:

Call A(0, 5), B(1, 2.5) and C(-10, 1) the 3 points of the triangle.
Prove that the line AC is perpendicular to the line AB by showing that their slope product is (-1).
Slope of AC: `a = (5 - 1)/(0 + 10) = 4/10 = 1/2.5`
Slope of line AB: `b = (5 - 2.5)/(0 - 1) = 2.5/-1 = -2.5`
The product ab = -1 . therefor, the 2 lines are perpendicular.