Question

The line joining the points (2, 1) and (5, - 8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0 Find the value of k.​

Answer 1

Step-by-step explanation:

Let A and B be (2,1) and (5,−8) respectiviey

∴

AB

AP

=

2

1

Section Formula: If point (x,y) divides line joining two points in (x

1

,y

1

) and (x

2

,y

2

) in ratio m:n internally

⇒ x=

m+n

mx

2

+nx

1

y=

m+n

my

2

+ny

1

Here, x

1

=2,y

1

=1, x

2

=5,y

2

=−8 and m=1,n=2

⇒ x=

3

5+4

=3y=

3

−8+2

=−2

(x,y)=(3,−2)

The point lies on

⇒ 2x−y+k=0

⇒ 6+2+k=0

⇒ k=−8