Find a relation between x and y, if the points A(x, y), B(−5, 7) and C(−4, 5) are collinear.


Find a relation between x and y, if the points A(xy), B(5, 7) and C(4, 5) are collinear.  


Let A(x1 = xy1 = y), B(x2 = −5, y2 = 7) and C(x3 = −4, y3 = 5) be the given points.
The given points are collinear if


$\Rightarrow x(7-5)+(-5)(5-y)+(-4)(y-7)=0$

$\Rightarrow 7 x-5 x-25+5 y-4 y+28=0$

$\Rightarrow 2 x+y+3=0$

Hence, the required relation is 2x + y + 3 = 0.


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