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  • 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.

5.  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.

Answers (1)

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Let the point on the x-axis be P(x,0) and it divides it in the ratio k:1.

Then, we have

Section formula:

 P(x,y) = \left (\frac{kx_{2}+x_{1}}{k+1} , \frac{ky_{2}+y_{1}}{k+1} \right )

\implies \frac{ky_{2}+y_{1}}{k+1} = 0

k =-\frac{y_{1}}{y_{2}}  

Hence, the value of k will be: k =-\frac{-5}{5}= 1

Therefore, the x-axis divides the line in the ratio 1:1 and the point will be,

Putting the value of k=1 in section formula.

P(x,0) = \left ( \frac{x_{2}+x_{1}}{2}, 0 \right )

P(x,0) = \left ( \frac{1-4}{2}, 0 \right ) = \left ( \frac{-3}{2}, 0 \right )

Posted by

Divya Prakash Singh

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