Find the ratio in which the line joining the points $(6, 3)$ and $(3, - 5)$ is divide by the $x -$ axis.

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Solution

Given points are

$(x_{1}, y_{1}) = (6, 3)$

$(x_{2}, y_{2}) = (3, - 5)$

Let the ratio $m_{1} : m_{2}$

So,

Its divided by $X - a x i s$ .

So,

$y = 0$

Now,

Using ratio formula,

$(x, y) = (\frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}})$

So,

$y = 0$

Then,

$0 = \frac{m_{1} (- 5) + m_{2} \times 3}{m_{1} + m_{2}}$

$0 = - 5 m_{1} + 3 m_{2}$

$5 m_{1} = 3 m_{2}$

$\frac{m_{1}}{m_{2}} = \frac{3}{5}$

Hence, this is the answer.

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