Question

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

Answer 1

Answer:

Step-by-step explanation:

Let the point A(x,y) which lies on line joining P(6,−6) and Q(−4,−1) such that PA/PQ=2/5

Line segment PQ is divided by the point A in the ratio 2:3.

Step 1: Find coordinates of A(x,y)

x=  

m  

1

​

+m  

2

​

 

m  

1

​

x  

2

​

+m  

2

​

x  

1

​

 

​

 

x=(2(−4)+3(6))/(2+3)

=(−8+18)/5

=10/5=2

y=  

m  

1

​

+m  

2

​

 

m  

1

​

y  

2

​

+m  

2

​

y  

1

​

 

​

 

y=(2(−1)+3(−6))/5

=(−2−18)/5

=−20/5

=−4

Step 2: Point A also lies on the line 3x+k(y+1)=0

3(2)+k(−4+1)=0

6−3k=0

or k=2.