HOW TO FIND THE CENTROID OF A TRIANGLE

Find coordinates of the centroid of each triangle.

Problem 1 :

Solution:

Vertices X(0, 3), Y(-6, 0) and Z(0, 0)

Formula to find centroid of a triangle is

So, the centroid of the given triangle is (-2, 1).

Problem 2 :

Solution:

Vertices D(-5, 0), E(0, 6) and F(2, 0)

Formula to find centroid of a triangle is

So, the centroid of the given triangle is (-1, 2).

Problem 3 :

Solution:

Vertices P(0, 6), Q(-3, 0) and R(-6, 6)

Formula to find centroid of a triangle is

So, the centroid of the given triangle is (-3, 4).

Problem 4 :

Solution:

Vertices K(5, 0), L(-2, 0) and M(0, -6)

Formula to find centroid of a triangle is

So, the centroid of the given triangle is (1, -2).

Find the coordinates of the centroid of each triangle given the three vertices.

Problem 5 :

C(-7, -6), B(-8, 0), A(0,0)

Solution:

Formula to find centroid of a triangle is

So, the centroid of the triangle is (-5, -2).

Problem 6 :

S(0, -6), R(-10, -6), Q(1,0)

Solution:

Formula to find centroid of a triangle is

So, the centroid of the triangle is (-3, -4).

Problem 7 :

T(0, 0), U(1, 3), V(-2,0)

Solution:

Formula to find centroid of a triangle is

So, the centroid of the triangle is (-1/3, 1).

Problem 8 :

Y(3, 4), X(-5, 0), W(0,0)

Solution:

Formula to find centroid of a triangle is

So, the centroid of the triangle is (-2/3, 4/3).

Problem 9 :

Two vertices of a triangle are (0, 0) and (9, 0). The centroid is (6, 1). Find the third vertex of the triangle.

Solution:

Given vertices of triangle (0, 0), (9, 0) (x₃, y₃) and G(6, 1)

Hence, the third vertex of the triangle is (9, 3).