Question

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

Answer 1

If given points are collinear then area of triangle formed by them must be zero.
$\Rightarrow$ $\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0$
$\Rightarrow$ $\frac{1}{2}\left[x\right(2-0)+1(0-y)+7(y-2\left)\right]=0$
$\Rightarrow$ $2x-y+7y-14=0$
$\Rightarrow$ $2x+6y-14=0$
$\Rightarrow$ $x+3y-7=0$
The last equation gives the relation between x and y.