# Point a Lies on the Line Segment Pq Joining P(6, -6) and Q(-4, -1) in Such a Way that (Pa)/( Pq)=2/5 . If that Point a Also Lies on the Line 3x + K( Y + 1 ) = 0, Find the Value of K. - Mathematics

Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that (PA)/( PQ)=2/5 . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.

#### Solution

Let the coordinates of A be(x,y) Here  (PA)/(PQ) = 2/5 . so ,

PA + AQ= PQ

⇒PA +AQ =(5PA)/2               [∵ PA = 2/5 PQ]

 ⇒AQ = (5PA)/2 - PA

⇒ (AQ)/(PA) = 3/2

⇒ (PA)/(AQ) = 2/3

Let (x, y) be the coordinates of A, which dives PQ in the ratio 2 : 3 internally Then using section formula, we get

 X = (2 xx (-4) +3 xx (6))/(2+3) = (-8+18)/5= 10/5 = 2

y = (2 xx (-1) + 3 xx(-6))/(2+3) = (-2-18)/5 = (-20)/5 = -4

Now, the point ( 2, -4 )  lies on the line 3x +k(y+1) = 0 ,therefore

3 × 2 +k(-4+1)=0

⇒ 3k = 6

⇒ k =6/3 =2

Hence, k=2.

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 4