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

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

1.	Find the relation between x and y if points (x,y),(1,2) and (7,0) are collinear.
Answer» If the given points are collinear, then the area of the triangle with these points as vertices will be zero.{tex}\\therefore{/tex}{tex}\\frac{1}{2}{/tex}[x (2 – 0) + 1 (0 – y) + 7(y –2)] = 0{tex}\\Rightarrow{/tex}{tex}\\frac{1}{2}{/tex}[2x – y + 7y –14] = 0{tex}\\Rightarrow{/tex}{tex}\\frac{1}{2}{/tex}[2x + 6y –14] = 0{tex}\\Rightarrow{/tex} 2x + 6y – 14 = 0{tex}\\Rightarrow{/tex} x + 3y – 7 = 0 .............Dividing throughout by 2This is the required relation between x and y.