**1. Internal division**

Consider a point P(x, y) divides the line segment joining A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m : n.

Draw

The coordinates of point P are

** Example:** Find the coordinates of point P which divides the line segment joining A(5, 3) and B(2, 1) in the ratio 5 : 2.

__Solution:__

**2. External division**

Consider a point P(x, y) divides the line segment joining A(x_{1}, y_{1}) and B(x_{2}, y_{2}) externally in the ratio m : n such that AP : BP = m : n.

Draw

The coordinates of point P are.

__Example:__

Find the coordinates of point which divides the line joining A(5, 2) and B(–1, 2) externally in the ratio 3 : 1.

__Solution:__

**3. Centroid of a triangle**

A Centroid of a triangle is the point where the ** three medians of the triangle meet**. The centroid of the triangle is also called as the

**of the triangle, which is shown as follows:**

*gravity*Here, **G** is the centroid of a triangle ABC.

**4. Median of a triangle**

The median of a triangle is a line segment joining a vertex and the midpoint of the opposite side of a triangle, which is shown as follows:

Here, are the three medians intersect at a single point G.

__Properties of Centroid of a triangle__

- Centroid is the centre of the object.
- Centroid is also known as gravity, geo centre and bary centre.
- Centroid of a triangle represents the interior of the triangle.

*The formula for the Centroid of a triangle of points A, B and C is: *

__Example:__

Find the centroid coordinates of the triangle whose vertices areis determined as follows:

__Solution__

Consider the centroid formula:

Let, substitute the value as follows:

Therefore, the centroid coordinates of the triangle is (2, 3).

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