Question

In what ratio is the segment joining the points A(4, 6) and B(−7, −1) divided by x-axis?

(a) 3 : 1
(b) 6 : 1
(c) 1 : 2
(d) 2 : 3

Answer 1

(b) 6 : 1
Let AB be divided by x-axis in the ratio k : 1 at the point P.
Then, by section formula, the coordinates of P are
$P\left(\frac{-7k+4}{k+1},\frac{-k+6}{k+1}\right)$
But P lies on the x-axis. So, its ordinate is 0.
Therefore,
$$\begin{gathered} \frac{-k+6}{k+1}=0 \\ \Rightarrow -k+6=0 \\ \Rightarrow k=6 \end{gathered}$$
Hence, the required ratio is 6 : 1.