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

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

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If the points (x, y), (1, 2)\ and\ (7, 0) are collinear then, the area formed by these points will be zero.

The area of the triangle is given by,

Area = \frac{1}{2}\left [ x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}) \right ] = 0

Substituting the values in the above equation, we have

Area = \frac{1}{2}\left [ x(2-0)+1(0-y)+7(y-2) \right ]= 0

\Rightarrow 2x-y+7y-14= 0

Or, 

\Rightarrow x+3y-7= 0

Hence, the required relation between x and y is x+3y-7= 0.

Posted by

Divya Prakash Singh

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