For what value of x are the points A (_3,12),B (7,6),C (x,9) collinear

1.	For what value of x are the points A (_3,12),B (7,6),C (x,9) collinear ?
Answer» According to the question, A(-3, 12), B(7, 6) and C(x, 9).(x1 = -3, y1 = 12), (x2 = 7, y2 = 6) and\xa0(x3 = x, y3 = 9)The given points A,B,C are collinear. So, area of triangle is zero.{tex}\\Rightarrow{/tex}\xa0x1(y2 - y3) + x2(y3 - y1)+ x3(y1 - y2)=0{tex}\\Rightarrow{/tex}\xa0{tex}(-3)(6 - 9) + 7 (9 - 12) +x(12 - 6) =0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}9 - 21 + 6x = 0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}6x = 12\xa0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}x = 2{/tex}

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