Find the value of x for which the points (x, -1), (2, 1) and (4, … - Vidyadip

Question

Find the value of x for which the points (x, -1), (2, 1) and (4, 5) are collinear.

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Answer

The given points are A(x, -1), B(2, 1) and C(4, 5) It is given that the points are collinear. So, the area of triangle that they form must be zero. Hence, $\text{x}_1(\text{y}_1-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)=0 \ ...(\text{i})$ Putting the value of $(\text{x}_1\text{y}_1),(\text{x}_2\text{y}_2),(\text{x}_3\text{y}_3)$ in ...(i) $\text{x}(1-5)+(2)(5-(-1))+4(-1-1)=0$ $-4\text{x}+2(5+1)+4(-2)=0$ $-4\text{x}+12-8=0$ $-4\text{x}=-12+8$ $-4\text{x}=-4$ $\text{x}=1$

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