Let us calculate the area of triangular region formed by the three points (1, 4), (–1, 2) and (–4, 1)

Question

Philoid · Accepted Answer

Area of triangle is given by formula

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

Where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are vertices of triangle

Here,

(x₁, y₁) is (1, 4)

⇒ x₁ = 1 and y₁ = 4

(x₂, y₂) is (-1, 2)

⇒ x₂ = -1 and y₂ = 2

(x₃, y₃) is (-4, 1)

⇒ x₃ = -4 and y₃ = 1

Hence substituting values in formula for area we get

Area = × [1(2 – 1) + (-1)(1 – 4) + (-4)(4 – 2)]

Area = × [1 + 3 + (-8)]

Area = × (-4)

Area = -2

Area cannot be negative

Area = 2 unit²