Question

solve the problem !!​

Answer 1

Let they are divided into $\bold{m_1 \: and \: m_2}$

Let the coordinates of X be (x,0)

By section formula we know,

$\boxed{y= \dfrac{m_1 \times y_2 + m_2 \times y_1}{m_1 + m_2}}$

$\mathsf{0 = \dfrac{m_1 \times 6 + m_2 \times (-3)}{m_1 + m_2}}$

$\mathsf{0 = \dfrac{6 m_1 - 3 m_2 }{m_1 + m_2}}$

On cross multiplying we get,

$\mathsf{0 = 6 m_1 - 3 m_2}$

$\mathsf{3m_2= 6 m_1 }$

$\mathsf{\dfrac{3}{6}= \dfrac{m_1}{m_2}}$

$\mathsf{\dfrac{1}{2}= \dfrac{m_1}{m_2}}$

So, the ratio in which they are divided is 1:2.

For coordinate of x,

$\boxed{x = \dfrac{m_1 \times x_2 + m_2 \times x_1}{m_1 + m_2}}$

$\mathsf{x = \dfrac{1 \times 5 + 2 \times 2}{2+1}}$

$\mathsf{x = \dfrac{5 + 4}{3}}$

$\mathsf{x = \dfrac{9}{3}}$

$\boxed{x = 3}$

So, coordinates of x axis are (3,0)