Question

In what ratio does the x-axis divide the join of A(2, −3) and B(5, 6)?

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

Answer 1

(c) 1 : 2
Let AB be divided by the x axis in the ratio $k:1$ at the point P.
Then, by section formula, the coordinates of P are
$P\left(\frac{5k+2}{k+1},\frac{6k-3}{k+1}\right)$
But P lies on the x axis: so, its ordinate is 0.
$\frac{6k-3}{k+1}=0$
$\Rightarrow 6k-3=0$
$\Rightarrow 6k=3$
$\Rightarrow k=\frac{1}{2}$
Hence, the required ratio is $\frac{1}{2}:1$, which is same as 1 : 2.