Q. 115.0( 4 Votes )
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.
Given: points P (3, 3) and Q (6, - 6).
Line 2x + y + k = 0
To find: The value of k.
If point P (x, y) divides the line segment A(x1, y1) and B(x2,y2)
Then the coordinates of P are:
Here, given points are P (3, 3) and Q (6, - 6) which is trisected at the points A (x1 , y1) and B(x2 , y2) such that A is nearer to P.
By section formula,
For point A (x1, y1) of PQ, where m = 2 and n = 1,
∴ 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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