Question

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Answer 1

Answer:

If the point P (2, 1) lies on the segment joining Points A (4, 2) and B (8, 4) then

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+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let P divide AB in the ratio k:1

Substituting (x

1

,y

1

)=(4,2) and (x

2

,y

2

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

P=(

k+1

k(8)+1(4)

,

k+1

k(4)+1(2)

)

But given P=(2,1)

⇒(

k+1

8k+4

,

k+1

4k+2

)=(2,1)

Comparing the x - coordinate,

⇒

k+1

8k+4

=2

⇒8k+4=2k+2

6k=−2

k=−

3

1

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

⇒

PB

AP

=

3

1

⇒AP=

2

1

AB

Answered