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  • Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (– 2, – 5) and (6, 3). Find the coordinates of the point of intersection.    

Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (– 2, – 5) and (6, 3). Find the coordinates of the point of intersection.

 

 
 
 
 
 

Answers (1)

Let the line x-3y = 0  intersect the segment AB where points A(-2,-5) and B(6,3) in the ratio k:1

So, coordinates of P are 

\left(\frac{6k-2}{k+1}, \frac{3k-5}{k+1} \right ).

P lies on the line x - 3y = 0

So,

\Rightarrow \frac{6k-2}{k+1}= 3\left ( \frac{3k-5}{k+1} \right )

\Rightarrow 6k-2 = 9k - 15

\Rightarrow 3k = 13

So the ratio is 13:3

\Rightarrow Coordinates of P are

 \left(\frac{9}{2}, \frac{3}{2} \right ).

Posted by

Safeer PP

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