# Determinants, Application of Determinants, Area of a Triangle, Condition of Collinearity of Three Points, Equation of a Line Passing through the Given Two Points

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## Application of Determinants

Determinant is used to find area of a triangle.

## Area of a Triangle

We know that area of a triangle , (say) whose vertices are and is given by

Area of

Also, [expanding along ]

From (1) and (2)

Area of

Thus the area of a triangle having vertices as and is given by

## Condition of Collinearity of Three Points:

Let and be three points then

C are collinear if area of

## Equation of a Line Passing through the Given Two Points:

Let the two points be and and be any point on the line joining and since the points and are collinear.

Thus the equation of the line joining points and is given by

Example 1:

Find the area of the triangle with vertices and

Solution:

sq. units.

Example 2:

Show that points and are collinear

Hence, the given points are collinear.

Example 3:

Find equation of the line joining and using determinants.

Solution:

Let be any point on the line joining and . Then

This is the required equation of line .