Question

The ratio in which the point P(6, −6) divides the line segment joining A(1, 4) and B(9, −12) is

(a) 2 : 3
(b) 3 : 2
(c) 3 : 5
(d) 5 : 3

Answer 1

(d) 5 : 3
Let the required ratio be k : 1.
Then, by section formula, the coordinates of C are
$P\left(\frac{9k+1}{k+1},\frac{-12k+4}{k+1}\right)$
Therefore,
$$\begin{gathered} \frac{9k+1}{k+1}=6\text{and}\frac{9k+1}{k+1}=-6\left[\text{Since}P\left(6,-6\right)\text{is given}\right] \\ \Rightarrow 9k+1=6k+6\text{and}9k+1=-6k-6 \\ \Rightarrow 3k=5\text{and}-6k=-10 \\ \Rightarrow k=\frac{5}{3}\text{in each case.} \end{gathered}$$
Therefore, the required ratio is $\frac{5}{3}:1$, which is same as 5 : 3.