Ch. 12 Determinants - 2

12.9


Determinants coordinate geometry


The area of a triangle having vertices at (x1,y1), (x2,y2) an d(x3,y3) us given by
Δ = determinants of

|x1 y1 1|
|x2 y2 1| *(1/2)
|x3 y3 1|

Condition of collinearity of three points:
Let the three points be (x1,y1), (x2,y2) and (x3,y3). The area of triange formed by these three points is zero. Hence the determinant

|x1 y1 1|
|x2 y2 1| will be zero
|x3 y3 1|

Equation of a line passing through two points:
Let the two points be (x1,y1), (x2,y2). If (x,y) is a point on the line passing through these two points, then (x1,y1), (x2,y2) and (x,y) are collinear. Hence the determinant
|x y 1|
|x1 y1 1|
|x2 y2 1| will be zero