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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
= 1/2[a(c+a)-b(b+c)+b(a+b)-c(c+a)+c(b+c)-a(a+b)]
Hence the points are collinear.

Directions: Solve the following problems.
Q 1: Prove that the points (4,2), (7,5) and (9,7) are collinear.

Question 2: This question is available to subscribers only!

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