Question

Find the value of $a$, if the points $P(1,5),Q(a,1)$ and $R(4,11)$ are collinear.

Answer 1

As the three points are collinear: $PQ+QR=PR$ and $PQ$ and $PR$ will have the same slope.

Slope of $PQ=\frac{5-1}{1-a}$ (1)

Slope of $PR=\frac{5-11}{1-4}$ (2)

Equating (1) and (2) gives

$\frac{4}{1-a}=\frac{-6}{-3}$

$2=\frac{4}{1-a}$

$1-a=2$

Hence $a=-1$