Question

Find the area of triangle whose vertices are (a, c + a), (a, c) and (–a, c – a).

Answer 1

We know area of triangle formed by three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by `triangle = 1/2 [x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`

The vertices are given as (a, c + a), (a, c) and (−a, c − a)  

`Δ = 1/2[a (c-c+a) + a(c-a-c-a)-a(c+a-c)`

`= 1/2[a(a)+a(2a)-a(a)]`

`= 1/2 [-2a^2]=a^2`