Find the value of x for which the points (x, –1),
Question:

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

Solution:

If points A (x, –1), B (2, 1), and C (4, 5) are collinear, then

Slope of AB = Slope of BC

$\Rightarrow \frac{1-(-1)}{2-x}=\frac{5-1}{4-2}$

$\Rightarrow \frac{1+1}{2-x}=\frac{4}{2}$

$\Rightarrow \frac{2}{2-x}=2$

$\Rightarrow 2=4-2 x$

$\Rightarrow 2 x=2$

$\Rightarrow x=1$

Thus, the required value of x is 1.

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