The line segment joining the points P (3, 3) and Q (6, - 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
Here, given points are P (3, 3) and Q (6, - 6) which is trisected at the points(say) A(x1 , y1) and B(x2 , y2)such that A is nearer to P.
By section formula,
x = 
, y = 
For point A(x1 , y1) of PQ, where m = 2 and n = 1,
x1 = 
, y1 = 
∴ x1 = 4 , y1 = 0
∴Coordinates of A is (4,0)
It is given that point A lies on the line 2x + y + k = 0.
So, substituting value of x and y as coordinates of A,
2 × 4 + 0 + k = 0
∴ k = - 8
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