Question

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

Answer 1

Answer:

5:9

Step-by-step explanation:

We know that,

Any point on the x-axis will be (x,0)

Let the ratio be k:1

Using section formula,

y = (m1y2 + m2y1)/m1 + m2

0 = (9k - 5)/k+1      ---1

In 1,

9k - 5 = 0

k = 5/9

therefore ratio = k:1

ie 5/9 : 1

ie 5 : 9

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Answer 2

Let the ratio be = k:1

Use the section formula, which states:

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

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