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Question
Find the value of x for which points A(x, 2), B(-3, -4) and C(7, -5) are collinear.
Solution
` "Let" A(x_1,y_1) = A(x,2) ,B (x_2,y_2)=B(-3,-4) and (x_3,y_3) = c=(7,-5) `.So the condition for three collinear points is
`x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0`
⇒ x(-4+5)-3(-5-2)+7(2+4)=0
⇒ x+21+42=0
⇒ x=-63
Hence , x= -63
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