Question

In what ratio does the point P(1, 2) divide the join of A(−2, 1) and B(7, 4)?

(a) 1 : 2
(b) 2 : 1
(c) 3 : 2
(d) 2 : 3

Answer 1

(a) 1 : 2
Let the required ratio be k : 1.
Then, by section formula, the coordinates of P are
$P\left(\frac{7k-2}{k+1},\frac{4k+1}{k+1}\right)$
Therefore,
$\frac{7k-2}{k+1}=1\text{and}\frac{4k+1}{k+1}=2\left[\text{Since}P\left(1,2\right)\text{is given}\right]$
$\Rightarrow 7k-2=k+1\text{and}4k+1=2k+2$
$\Rightarrow 6k=3\text{and}2k=1$
$\Rightarrow k=\frac{1}{2}$ in each case
So, the required ratio is $\frac{1}{2}:1$, which is same as 1 : 2.