The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is

Question

Philoid · Accepted Answer

Let the vertices of a triangle = A, B and C

Where;

A = (x₁, y₁) = (a, b + c)

B = (x₂, y₂) = (b, c + a) and

C = (x₃, y₃) = (c, a + b)

∵ Area of

[x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

[a(c - b) + b(a - c) + c(b - a)]

[ac - ab + ab - bc + bc - ac] = (0) = 0

Hence, the area of triangle is 0.