Find the centroid of Δ ABC whose vertices are A(– 1, 0), B(5, – 2) and C(8, 2)

Question

Find the centroid of &Delta; ABC whose vertices are A(&ndash; 1, 0), B(5, &ndash; 2) and C(8, 2)

Philoid · Accepted Answer

First we need to calculate the coordinates of median

For coordinates of median AD segment BC will be taken

X = (m₁x₂ + m₂x₁)/ m₁ + m₂

= (1 × 8 + 1x 5)/1 + 1

= (8 + 5) /2

= 13/2

Y = (m₁y₂ + m₂y₁)/ m₁ + m₂

= (1x 2 + 1x (– 2))/2

= (0)/2

= 0 / 2 = 0

D(13/2,0)

The centroid of the triangle divides the median in the ratio 2:1

By section formula,

X = (m₁x₂ + m₂x₁)/ m₁ + m₂

= (2 × 13/2 + 1x (– 1))/2 + 1

= (13 – 1) /3

= 12/3 = 4

Y = (m₁y₂ + m₂y₁)/ m₁ + m₂

= (2x 0 + 1x 0)/2 + 1

= 0/3

= 0

∴ G coordinate is (4, 0)