Question

point a lies on the line segment pq where p(6,-6) and q(-4,-1)in such a way that pa/pq=2/5.if point p also lies on the line 3x+k(y+1)=0. find value of k

Answer 1

Answer:

Step-by-step explanation:

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PA/PQ=2/5

or, PA/(PA+AQ)=2/5

or, 5PA=2PA+2AQ

or, 5PA-2PA=2AQ

or,3PA=2AQ

or, PA/AQ=2/3

or, m:n=2:3

If the coordinates of A is (x,y) the,

x=(mx₂+nx₁)/(m+n) and y=(my₂+ny₁)/(m+n)

Here, (x₁,y₁)=(6,-6), (x₂,y₂)=(-4,-1)

∴, x={2×(-4)+3×6)}/(2+3)

=(-8+18)/5

=10/5

=2

y={2×(-1)+3×(-6)}/(2+3)

=(-2-18)/5

=-20/5

=-4

Now, p(2,-4) lies on 3x+k(y+1)=0 then 

3×2+k(-4+1)=0

or, 6+k(-3)=0

or, -3k=-6

or, k=2 Ans.

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