Question

if the point p(2 1) lies on the line segment joining points a(4 2) and b(8 4) then the ratio of ap:pb is​

Answer 1

Answer:

Using the section formula, if a point (x,y) divides the line joining the points (x 1 ,y 1 ) and (x

2,y 2 ) in the ratio m:n, then

(x,y)=( m+nmx 2 +nx 1 ,m+nmy 2 +ny 1)

Let P divide AB in the ratio k:1

Substituting (x 1 ,y 1 )

=(4,2) and (x2,y )

=(8,4) in the section formula, we get

P=( k+1k(8)+1(4) ,k+1k(4)+1(2)

But given P=(2,1)

⇒( k+18k+4,k+14k+2)=(2,1)

Comparing the x - coordinate,

⇒

k+1

8k+4

=2

⇒8k+4=2k+2

6k=−2

k= -1/3

As k is negative, P divides AB in the ratio 1:3 externally.

⇒ AP / PB= 1/ 3

⇒AP= 1/2 AB .

Step-by-step explanation:

hope you understood