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

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

Let (x, y), (1, 2) and (7, 0) are vertices of a triangle,

Area of triangle = \( \frac{1}{2} \ | \ [ (x_1(y_2 – y_3 ) + x_2(y_3 – y_1) + x_3(y_1 – y_2) ) ] \ | \ = \ 0 \)

\( \Rightarrow \frac{1}{2} \ | \ [x(2 – 0) + 1 (0 – y) + 7( y – 2)] \ | \ = \ 0 \)

\( \Rightarrow 2x \ – \ y \ + \ 7y \ – \ 14 \ = \ 0 \)

\(\Rightarrow 2x \ + \ 6y \ – \ 14 \ = \ 0 \)

\(\Rightarrow x \ + \ 3y \ – \ 7 \ = \ 0 \) .