Question

In what ratio does the point P(2, −5) divide the line segment joining A(−3, 5) and B(4, −9)?

(a) 3 : 2
(b) 2 : 1
(c) 5 : 2
(d) 5 : 3

Answer 1

(c) 5 : 2

Let the required ratio be k : 1.
Then, by section formula, the co-ordinates of P are
$P\left(\frac{4k-3}{k+1},\frac{-9k+5}{k+1}\right)$
∴ $\frac{4k-3}{k+1}=2\mathrm{and}\frac{-9\mathrm{k}+5}{\mathrm{k}+1}=-5$ [ Since P(2, -5) is given]
⇒ 4k - 3 = 2k + 2 and -9k + 5 = - 5k - 5
⇒ 2k = 5 and 4k = 10
∴ $k=\frac{5}{2}$ in each case.
So, the required ratio is $\frac{5}{2}:1$, which is 5 : 2.