# Worksheet on Centroid of a Triangle

Different types of questions are given under the worksheet on centroid of a triangle.

Let us recall the formula for finding the centroid of a triangle as follows;

The co-ordinates of the centroid of the triangle formed by joining the points (x₁, y₁) , (x₂, y₂) and (x₃, y₃) are

({x₁ + x₂ + x₃}/3 , {y₁ + y₂ + y₃}/3

Here two varieties of questions are given:

(i) using the formula to find the centroid of a triangle where three vertices are given

(ii) for finding the third vertex where centroid of a triangle is given along with the co-ordinates of its two vertices

1. Find the co-ordinates of the centroid of the triangle formed by the following sets of three points:

(i) (7, 5), (- 2, 5) and (4, 6)

(ii) (4, - 1), (0, 3) and (- 4, - 2)

(iii) (3, - 4), (4, 7) and (2, 9) .

2. Show that the origin is the centroid of the triangle formed by the points (x - y, y - z),(- x, - y) and (y, z).

3. Find the co-ordinates of the point of intersection of the medians of the triangle formed by joining the points (-1, - 2), (8, 4) and (5, 7).

4. The co-ordinates of the vertices of a triangle are (4, - 3), (- 5, 2) and (x, y). If the centre of gravity of the triangle is at the origin find x, y.

5. The centroid of a triangle is (- 1, - 2) and co-ordinates of its two vertices are (4, 6) and (- 8, - 12). Find the co-ordinates of its third vertex.

6. The co-ordinates of the vertex A of the ∆ ABC are (2, 5); if the centroid of the triangle is at (-2, 1), find the co-ordinates of the mid-point of the side BC.

Answers for the worksheet on centroid of a triangle are given below to check the exact answers of the above questions on mid-point.

1. (i) (3, 2)

(ii) (0, 0)

( iii) (3, 4)

3. (4, 3)

4. x = 1 , y = 1

5. (1, 0)

6. (-4, -1)

Co-ordinate Geometry