Slope (m) of a line = (y2-y1)/(x2-x1) So for line AB, the slope is (3-2)/(-1-1) = 1/-2 = -1/2 For line AC = (3--1)/(-1--3) = (3+1)/(3-1) = 4/2 = 2 For line BC = (2--1)/(1--3) = (2+1)/(1+3) = 3/4 In order for an angle (<) to be right, it must be 90°, so the two lines making the right angle must be perpendicular. Perpendicular lines by definition have slopes that are the negative reciprocal. That means that you change the sign of one line's slope (m) and divide 1 by it: m2 = 1/-m1 So for lines AB and AC: m(AC) = 1/-m(AB), does 2 = 1/--1/2? YES!! 1/--1/2 = 1/1/2 = 2, so < BAC is 90° and therefore a right < How about for lines AB and BC: m(BC) = 1/-m(AB), does 3/4 = 1/--1/2? NO, because 1/--1/2 = 1/1/2 = 2, not = to 3/4, so < ABC is not right How about our last < BCA: m(AC) = 1/-m(BC), does 2 = 1/-3/4? NO, because 1/-3/4 = -4/3, not = to 2, so < BCA is not right So yes, the triangle is a right triangle because < BAC is right (=90°)!
