Find a relation between x and y, if the points

Question:

Find a relation between x and y, if the points A(2, 1), B(xy) and C(7, 5) are collinear.

Solution:

Let A(x1 = 2, y1 = 1), B(x2 = xy2 = y) and C(x3 = 7, y3 = 5) be the given points.
The given points are collinear if

$x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

$\Rightarrow 2(y-5)+x(5-1)+7(1-y)=0$

$\Rightarrow 2 y-10+4 x+7-7 y=0$

$\Rightarrow 4 x-5 y-3=0$

Hence, the required relation is 4x − 5y − 3 = 0.

 

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