Question

If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (– 1, 2) and (3, 2). Find the centroid of the triangle.

Answer 1

Let the triangle be ABC with vertex A(1, 1) and midpoint of AB is E (– 1, 2), midpoint of AC is F (3, 2). Let (x₁ y₁) and (x₂, y₂) be the co-ordinate of B and C respectively. Since E is the midpoint of AB.

\(\therefore (\frac{1+x_1}{2},\frac{1+y_1}{2})=(-1,2)\)

⇒ x₁ = − 3, y₁ = 3

 And F is the midpoint of AC

\(\therefore (\frac{1+x_2}{2},\frac{1+y_2}{2})=(3,2)\)

⇒ x₂= 5, y₂ = 3

∴ Centroid of the triangle have co-ordinates

\((\frac{1-3+5}{3},\frac{1+3+3}{3})=(1,\frac{7}{3})\)