Let us prove that the line joining two points (1, 2) and (–2, –4) passes through origin.

Let the points be

A = (x₁, y₁) = (1, 2) and

B = (x₂, y₂) = (-2, -4)

Let O be the origin

O = (x₃, y₃) = (0, 0)

Now if the area of triangle formed by joining point A, O and B i.e. ΔAOB is zero then we can say that points A, O and B are collinear which means they lie on the straight line which would imply that line passing through A and B will pass through origin O

So we have to prove that area(ΔAOB) = 0

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

Substituting values

⇒ Area = × [1(-4 – 0) + (-2)(0 – 2) + 0(2 – (-4))]

⇒ Area = × [-4 + 4 + 0]

⇒ Area = 0

Hence, line joining two points (1, 2) and (–2, –4) passes through origin.