# Point A lies on the line segment PQ joining P(6, – 6) and Q(– 4, – 1) in such a way that . If the point A also lies on the line 3x + k(y + 1) = 0, find the value of k.

Let the point P(x,y) divides AB

Then

X = (m1x2 + m2x1)/ m1 + m2

= (2 × (– 4) + 3 × 6)/2 + 3

= (– 8 + 18) /5

= 10/5 = 2

Y = (m1y2 + m2y1)/ m1 + m2

= (2 × (– 1) + 3 x( – 6))/ 5

= (– 2 – 18)/5

= – 20 / 5 = – 4

If the point A also lies on the line 3x + k(y + 1) = 0

Then

3 × 2 + k(– 4 + 1) = 0

6 – 3k = 0

6 = 3k

k = 2

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