Question

The line segment joining the points P (3, 3) and Q (6, - 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

Answer 1

Step-by-step explanation:

P(3,3),Q(6,-6)

PA=AB=BO

PA:AO=1:2

The coordinates of A are given to be

(1×6+2×3/1+2,1×(-6)+2×3/1+2)

(6+6/3,-6+6/3)

(12/3,0/3)=(4,0)

2x+y+k=0 passes through A therefore,

2(4)+0+k=0

8+k=0

k=-8

Answer 2

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

hope it will help you.......❣️