Question

if x- axis divides the line (2, -5) and (1, 9) in the ratio​

Answer 1

Let the ratio be = k:1

Use the section formula, which states:

$\red{\sf{ (x, y) = (\frac{mx_{1}+ nx_{2}}{m+n}, \frac{my_{1}+ ny_{2}}{m+n} ) }}$

We note down the information given to us:

• $\sf{( x_{1}, y_{1}) = (2,-5)}$

• $\sf{( x_{2}, y_{2} = (1,9)}$

• m:n = k:1

• (x,y) = (x,0)

We put in the values and then we find:

$\sf{ (x, 0) = (\frac{2k + 1}{k+1}, \frac{-5k + 9}{k+1} ) }$

→ $\sf{ -5k + 9 = 0}$

→ k = 9/5

Thus, ratio is 9:5