High School Mathematics - 2 9.21 Collinearity of Points
If three points (x1, y1), (x2, y2), (x3, y3) lie on a straight line, the area of the triangle formed by them is zero.
i.e1/2(x1y2-x2y1+x2y3-x3y2+x3y1-x1y3) = 0
Example: Show that the points (a,b+c),(b,c+a) and (c, a+b) are collinear.
The area of the triangle formed by the three points is
Hence the points are collinear.
Directions: Solve the following problems.