Question

Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

Answer 1

Solution: If given points are collinear then area of triangle formed by them must be zero.

Or, ½ [x1(y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)] = 0

Or, ½ [x(2 – 0) + 1 (0 – y) + 7( y – 2)] = 0

Or, 2x – y + 7y – 14 = 0

Or, 2x + 6y – 14 = 0

Or, x + 3y – 7 = 0

The last equation gives the relation between x and y.