Question

find the ratio in which the line segment joining A(1,-5), and B(-4,5) is divided by the x-axis. Also find the coordinates of the point of division.​

Answer 1

let the required ratio be $\boxed{ \bf k \: : \: 1}$
And,
the coordinates of the cutting point be $\boxed{\bf P = \: (x \: , \: 0) \: }$
Therefore,
As per Question,
$\boxed{ \tt P = \left( \frac{k - 4}{k + 1} , \frac{ - 5k + 5}{k + 1} \right) \: }$

Thus,
$\qquad \frac{ - 5k + 5}{k + 1} = 0 \\ \\ \implies - 5k + 5 = 0(k + 1) \\ \\ \implies - 5k + 5 = 0 \\ \\ \implies 5k = 5 \\ \\ \implies k = \frac{5}{5} = \frac{ \cancel{5}}{ \cancel{5}} \\ \\ \implies k = 1$

And,
$\qquad \frac{k - 4}{k + 1} = x \\ \\ \implies \frac{1 - 4}{1 + 1} = x \\ \\ \implies \frac{ - 3}{2} = x \\ \\ \implies x = - \frac{3}{2}$

Hence, the required ratio = k : 1 = 1 : 1

and the required coordinates $= (x.0) = \left( - \frac{3}{2} \: , \: 0 \right)$

Answer 2

Answer:

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