Question

in what ratio x-axis divide the Join of (2,-4),(-3,6) ? find the point of intersection also​

Answer 1

Let,

• x - axis divide the join of (2,-4),(-3,6) in ${m_1\: :\:m_2}$ ratio .

• and the point of intersection be→ P(x,0)

So,

$(x,0) = ( \frac{m_2 \times 2 + m_1 \times ( - 3)}{m_1\: + \:m_2}, \frac{m_2 \times ( - 4) + m_1 \times 6}{m_1\: + \:m_2} )$

$\bold{ \rightarrow(x,0) = ( \frac{2m_2 - 3m_1 }{m_1\: + \:m_2}, \frac{ - 4m_2 + 6m_1 }{m_1\: + \:m_2} )}$

• † That means ,

$\bold{ \rightarrow \: 0 = \frac{ - 4m_2 + 6m_1 }{m_1\: + \:m_2} }$

$\rightarrow \: 0 = - 4m_2 + 6m_1$

$\bold{\rightarrow \: 4m_2 = 6m_1 }$

$\rightarrow \: \bold{\frac{m_1}{m_2} \: = \frac{4}{6} }$

$\rightarrow \bold{ \boxed {\bold{ \: m_1\: :\:m_2 \: = 4 : 6}}}$

$\\ \\ \\ \large \frak {\underbrace { \color{blue}{\bold{So , the \: \: ratio \: \: is \: \: \: 4:6}}}}$

$\large\frak{And}$

$\large \color{red} \bold{ x = \frac{2m_2 - 3m_1 }{m_1\: + \:m_2}}$

$\bold{ \rightarrow} \: \large \color{red} \bold{ x = \frac{2 \times 6- 3 \times 4 }{4\: + \:6}}$

$\bold{ \rightarrow} \: \large \color{red} \bold{ x = \frac{12 \ - 12 }{10}}$

$\bold{ \rightarrow} \: \large \color{red} \bold{ x = \frac{0}{10}}$

$\bold{ \rightarrow} \: \large \color{green} \bold{ x = 0}$

$\large{ \boxed { \bf{ \bold{So, \: point \: of \: intersection \: \: P(x,0) \: → \: (0,0)}}}}$