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Question
Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7,5) are collinear.
Solution
Let `A(x_1 =2,y_1=1),B (x_2 =x,y_2=y) and C (x_3=7,y_3=5` be the given points .
The given points are collinear if
`x_1 (y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0`
`⇒2(y-5)+x(5-1)+7(1-y)=0`
`⇒2y-10+4x+7-7y=0`
`⇒ 4x-5y-3=0`
Hence, the required relation is 4x -5y-3=0
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