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Question
Find a relation between x and y, if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.
Solution
Let `A(x_1=x,y_1=y),B(x_2=-5,y_2=7) and C (x_3 =-4, 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`
`⇒ x(7-5)+(-5)(5-y)+(-4)(y-7)=0`
`⇒7x-5x-25+5y-4y+28=0`
`⇒ 2x +y+3=0`
Hence, the required relation is 2x +y+3 =0
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