Question

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

Answer 1

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

Slope of AB = Slope of BC

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

⇒ $\frac {1+1}{2-x}=\frac 42$

⇒ $\frac {2}{2-x}=2$

⇒ $2=4-2x$

⇒ $2x=2$

⇒ $x=1$

Thus, the required value of x is 1.