Question

The coordinates of the centroid of a triangle are (√3,2), and two of its vertices are (2√3,-1) and (2√3,5). Find the third vertex of the triangle.

Answer 1

Let the third vertex of a triangle be (x, y)

Here, x₁ = 2√3, x₂ = 2√3, x₃ = x

and y₁ = -1, y₂ = 5, y₃ = y

and the coordinates of the centroid is (√3, 2)

We know that

⇒ 4√3 + x = 3√3 and 4 + y = 6

⇒ x = -√3 and y = 2

Hence, the third vertex of a triangle is (-√3, 2)