If G(– 2, 1) is the centroid of a ΔABC and two of its vertices are A(1, – 6) and B(– 5, 2), find the third vertex of the triangle.

Question

Philoid · Accepted Answer

The figure is shonw as:

– 2 = (m₁x₂ + m₂x₁)/ m₁ + m₂

– 2 = (2 × x + 1x 1)/2 + 1

– 2 = (2x + 1) /3

– 6 = 2x + 1

– 7 = 2x

⇒ x = – 7/2

1 = (m₁y₂ + m₂y₁)/ m₁ + m₂

1 = (2x y + 1x (– 6))/3

1 = (2y – 6)/2

2 = 2y – 6

8 = 2y

⇒ y = 4

D(– 7/2,4)

Now for BC

– 7/2 = (m₁x₂ + m₂x₁)/ m₁ + m₂

– 7/2 = (1 × x + 1x (– 5))/1 + 1

– 7/2 = (x – 5) /2

– 7 = x – 5

– 7 + 5 = x

⇒ x = – 2

4 = (m₁y₂ + m₂y₁)/ m₁ + m₂

4 = (1 × y + 1x 2)/2

4 = (y + 2)/2

8 = y + 2

⇒ y = 6

Hence, C(– 2, 6)