Question

Find the relation between 'x' and 'y', if the points (x,y),(4,0) and (1,-6) are collinear.​

Answer 1

Let's assume these 3 points as the vertices of a triangle.

Now if lines are to be collinear, the area of a triangle formed by 3 sides must equals to zero.

A/q

Area of triangle:-

$\frac{1}{2} [x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y1_-y_2)] \\\\ Area of triangle=0 = \frac{1}{2} [x(0+6)+4(-6-y)+1(y-0)] \\\\ \frac{1}{2} [0+6x-24-4y+y]=\frac {6x-3y-24}{2} =0 \\\\ 6x-3y =24 \\\\ 6x= 24+3y \\\\ x= \frac{24+3y}{6}$