Question

Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7,5) are collinear.

Answer 1

Let `A(x_1 =2,y_1=1),B (x_2 =x,y_2=y) and  C (x_3=7,y_3=5` be the given points .

The given points are collinear if

`x_1 (y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0`

`⇒2(y-5)+x(5-1)+7(1-y)=0`

`⇒2y-10+4x+7-7y=0`

`⇒ 4x-5y-3=0`

Hence, the required relation is 4x -5y-3=0