Applications of Determinant in Geometry

1. Area of triangle If (x1, 71), (x2, Y2) and (x3, Y3 ) are the vertices of a triangle, then a

Vi Area of triangle Y 2 X1 1 X2 2

X3

1

1

Y3

1

= l< (24i ( 92 – 9;)+3 ( 93 – ») + x3( – 92)] [x1 73+ x2 y3 - 2

х 2. Condition of collinearity of three points Let three points be A(x1, y1), B(x2, Y2) and C(x3, Y3), then these points will be collinear, if Area of AABC = 0 3. Equation of straight line passing through two points Let two points be A(x1, y1) and B(x2, y2) and P(x, y) be a point on the line joining points A and B, then the equation of line is given by

1 X1 V1 1 = 0 х

X2 72 V

y

1