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  • The line segment joining the points A(2, 1) and B(5, - 8) is trisected by the points P and Q, where P is nearer to A. If the point P also lies on the line

The line segment joining the points A(2, 1) and B(5, - 8) is trisected by the points P and Q, where P is nearer to A. If the point P also lies on the line 2x - y + k = 0, find the value of k.

 

 

 

 
 
 
 
 

Answers (1)

P and Q are points of trisection and P is nearer to A.

\therefore AP : PB = 1 : 2

So, 

P=\left ( \frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n} \right )

     =\left ( \frac{1(5)+2(2)}{1+2}, \frac{1(-8)+2(1)}{1+2} \right )

     =\left ( \frac{9}{3}, \frac{-6}{3} \right )

\Rightarrow P\left ( 3 , -2 \right ) \text{passes through }2x-y+k=0

2(3)-(-2)+k=0

6+2+k=0

k=-8

Posted by

Ravindra Pindel

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