Question

11) If the popnt P (6, 2) divides the line segment
joining A (65) and Blu, y) in the ratio Bil.
then find the value of y.
​

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+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let the ratio be k:1

Substituting (x

1

,y

1

)=(−2,2) and (x

2

,y

2

)=(3,7) in the section formula, we get

(

k+1

k(3)+1(−2)

,

k+1

k(7)+1(2)

)=(2,y)

(

k+1

3k−2

,

k+1

7k+2

)=(2,y)

Comparing the x - coordinate,

⇒

k+1

3k−2

=2

⇒3k−2=2k+2

⇒k=4

Hence, the ratio is 4:1.

Comparing the y - coordinate,

⇒

k+1

7k+2

=y

⇒

4+1

7(4)+2

=y

⇒y=6

I hope it will help you