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
⇒ 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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