Question

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

Answer 1

If the given points are collinear, then the area of triangle formed by these points will be 0.

Area of Triangle = `1/2 {x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}`

Area = `1/2[x(2-0)+1(0-y)+7(y-2)]`

`0=1/2[2x-y+7y-14]`

`0=1/2[2x+6y-14]`

2x+6y-14=0

x+3y-7 =0

This is the required relation between x and y.