MCQ
The ratio in which the line segment joining points $A\left(a_1, b_1\right)$ and $B\left(a_2, b_2\right)$ is divided by $y-$axis is :
- ✓$ -a_1: a_2 $
- B$ a_1: a_2 $
- C$ b_1: b_2 $
- D$ -b_1: b_2 $
✓
Answer
Correct option: A.
$ -a_1: a_2 $
Let the point $P$ on $y-$axis, divides the line segment joining the point $A\left(a_1, b_1\right)$ and $B\left(a_2, b_2\right)$ is the ratio $m_1: m_2$ and let the co $-$ ordinates of $P$ be $(0, y),$
then $0=\frac{\text{m}_1\text{x}_2+\text{m}_2\text{x}_1}{\text{m}_1+\text{m}_2}$
$\Rightarrow\ 0=\frac{\text{m}_1\text{a}_2+\text{m}_2\text{a}_1}{\text{m}_1+\text{m}_2}$
$\Rightarrow\ \text{m}_1\text{a}_2+\text{m}_2\text{a}_1=0$
$\Rightarrow\ \text{m}_1\text{a}_2=-\text{m}_2\text{a}_1$
$\Rightarrow\ \frac{\text{m}_1}{\text{m}_2}=\frac{-\text{a}_1}{\text{a}_2}$
Ratio is $ -a_1: a_2$
then $0=\frac{\text{m}_1\text{x}_2+\text{m}_2\text{x}_1}{\text{m}_1+\text{m}_2}$
$\Rightarrow\ 0=\frac{\text{m}_1\text{a}_2+\text{m}_2\text{a}_1}{\text{m}_1+\text{m}_2}$
$\Rightarrow\ \text{m}_1\text{a}_2+\text{m}_2\text{a}_1=0$
$\Rightarrow\ \text{m}_1\text{a}_2=-\text{m}_2\text{a}_1$
$\Rightarrow\ \frac{\text{m}_1}{\text{m}_2}=\frac{-\text{a}_1}{\text{a}_2}$
Ratio is $ -a_1: a_2$
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