Question

The line segment PQ joining the points P (5,-2) and Q (1,3) is trisected at the points, A(x,-2) and B (⅔,y). Find the value of x & y.

​

Answer 1

Answer:

Let the coordinates of point A be (x  

1,

​  

y  

1

​  

)

Since A divides PQ in the ratio 1:2

So,    (x  

1,

​  

y  

1

​  

)=(  

1+2

1×6+2×3

​  

,  

1+2

1×−6+2×3

​  

)

                     = (  

3

6+6

​  

,  

3

−6+6

​  

)

                     =(4,0)

Since A lies on 2x+y+k=0

So, 2x  

1

​  

+y  

1

​  

+k=0

⇒2×4+0+k=0

⇒8+k=0

⇒k=−8