Question

If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x​

Answer 1

${\huge{\underline{\sf {\pink{Answer}}}}}$

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$\boxed{x \: = \: -23}$

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${\huge{\underline{\sf {\pink{Explanation :}}}}}$

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Given :

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A ( x , 2 ), B ( -3 , 4 ) and C ( 7 , 5 ) are collinear.

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To find :

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• Value of x

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Solution :

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We know, if $\sf({x}_{1} ,\: {y}_{1}) ,\: ({x}_{2}, \: {y}_{2}) ,\: ({x}_{3} ,\: {y}_{3})$are three collinear points then,$\sf{x}_{1}({y}_{2} - {y}_{3}) + {x}_{2}({y}_{3} - {y}_{1}) + {x}_{3}({y}_{1} - {y}_{2}) = 0$

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↬ $\sf \: x(4 - 5) + ( - 3)(5 - 2) + 7(2 - 4) = 0$

↬ $\sf \: x( - 1) + ( - 3)(3) + 7( - 2) = 0$

↬ $\sf \: (- x - 9 - 14) = 0$

↬ $\sf (- x - 23) = 0$

↬ $\sf - x = 23$

↬ $\sf \: x = - 23$