Question

The coordinates of the vertices of a triangle ABC are A (–7, 6), B(2, –2) and C(8, 5). Find coordinates of its centroid.

Solution: Suppose A(x₁, y₁) and B(x₂, y₂) and C(x₃, y₃)

 x₁ = –7, y₁ = 6 and x₂ = 2, y₂ = –2 and x₃ = 8, y₃ = 5

Using Centroid formula

∴ Coordinates of the centroid of a traingle

ABC = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`

= `(square/3, square/3)`

∴ Coordinates of the centroid of a triangle ABC = `(3/3, square)`

∴ Coordinates of the centroid of a triangle ABC = `(1 , square)`

Answer 1

Suppose A(x₁, y₁) and B(x₂, y₂) and C(x₃, y₃)

 x₁ = –7, y₁ = 6 and x₂ = 2, y₂ = –2 and x₃ = 8, y₃ = 5

Using Centroid formula

∴ Coordinates of the centroid of a traingle

ABC = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`

= `((-7 + 2 + 8)/3, (6 - 2 + 5)/3)`

∴ Coordinates of the centroid of a triangle ABC = `(3/3, 9/3)`

∴ Coordinates of the centroid of a triangle ABC = (1 , 3)