Question
Sat February 16, 2013 By: Anish Mishra
 

the line segment joining the points a(2,1)and b(5,-8)is trisected at the points p and q such as p is nearea to A.if p also lies on the line given by 2x-y+k=0.find the value of k.

Expert Reply
Sun February 17, 2013
The line segment AB is trisected by points P and Q. So, AP: PQ = 1: 2
 
Using section formula, the coordinates of point P are (1x5+2x2/1+2, 1x(-8)+2x1/1+2) = (3, -2)
Now, it is given that P lies on the line 2x - y + k = 0.
Therefore, we have:
2x3 - (-2) + k = 0
6+2+k=0
k=-8
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