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