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

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Q. The value of $x$ for which the points $(x,-1),(2,1)$ and $(4,5)$ are collinear, will be

Straight Lines

Solution:

Since, points are $A(x,-1), B(2,1)$ and $C(4,5)$ are collinear.
Here, $x_1=x, y_1=-1, x_2=2, y_2=1, x_3=4$ and $y_3=5$
Slope of $A B=$ Slope of $B C$
$ \Rightarrow \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}$
$ \Rightarrow \frac{1+1}{2-x}=\frac{5-1}{4-2}\left(\because \text { slope of line }=\frac{y_2-y_1}{x_2-x_1}\right)$
$ \Rightarrow \frac{2}{2-x}=\frac{4}{2} \Rightarrow 2-x=1 $
$\Rightarrow x=2-1=1 $