Question

The area of a triangle is 3 square units. Two of its vertices are A(3,1), B(1,-3) and the centroid of the triangle lies on x-axis. Find the coordinates of the third vertex C.

Answer 1

Given: Coordinates of Triangle are A(3, 1) and B(1, -3)

Centroid of triangle lies on x- axis.

Let the third coordinate be C(x, y)

Centroid of the triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃₎ is given by,

The y coordinate of centroid will be 0, as it lies opn x – axis.

Therefore,

y₁ + y₂ + y₃ = 0

1 – 3 + y₃ = 0

y₃ = 2

So, C(x, y) becomes (x, 2)

We are given that the area of triangle = 3 square units.

We know that,