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Answer :

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

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

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

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

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

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