Question
Write the ratio in which the line segment joining the points $A(3, -6)$ and $B(5, 3)$ is divided by $x-$axis.
✓
Answer
The point lies on $x-$axis.
Its ordinate will be $= 0$
Let the point $P(x, 0)$ divides the line segment joining the points $A(3, -6)$ and $B(5, 3)$ in the ratio $m : n.$
$\therefore\ 0=\frac{\text{my}_2+\text{my}_1}{\text{m}+\text{n}}\Rightarrow\ 0=\frac{\text{m}\times3+\text{n}(-6)}{\text{m}+\text{n}}$
$⇒ 3m - 6n = 0 ⇒ 3m = 6n$
$\Rightarrow\ \frac{\text{m}}{\text{n}}=\frac{6}{3}=\frac{2}{1}$
$\therefore$ Ratio $= 2 : 1$
Its ordinate will be $= 0$
Let the point $P(x, 0)$ divides the line segment joining the points $A(3, -6)$ and $B(5, 3)$ in the ratio $m : n.$
$\therefore\ 0=\frac{\text{my}_2+\text{my}_1}{\text{m}+\text{n}}\Rightarrow\ 0=\frac{\text{m}\times3+\text{n}(-6)}{\text{m}+\text{n}}$
$⇒ 3m - 6n = 0 ⇒ 3m = 6n$
$\Rightarrow\ \frac{\text{m}}{\text{n}}=\frac{6}{3}=\frac{2}{1}$
$\therefore$ Ratio $= 2 : 1$
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