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