Question

9. In what ratio is the line segment joining the points A(2, 4) and B(6,5) divided by the y-axis? (a) 2:1 (internally) (b) 2:1 (externally) (C) 3:1 (internally) (d) 3:1 (externally)​

Answer 1

Answer:

Given the points (3,4) and (2,6)

let the required ratio be K:1

⇒ By section formula

x=

m+n

mx

2

+nx

1

,y=

m+n

my

2

+ny

1

As x-axis divides (x,y) will be of the form (x,0)

x=

K+1

2K+3

,y=

K+1

6K+4

⇒

K+1

6K+4

=0

⇒6K=−4

∴K=

3

−2

∴2:3

externally

∴ putting the value of K in (x,Y)

x=

K+1

2K+3

=

3

−2

+1

2x−

3

−2

+3

=

3

−2+3

3

−4+9

=5

y=

K+1

6K+4

=

3

−2

+1

6×

3

−2

+3

=

3

−2+3

3

−12+9

=−3

∴(x,y)=(5,−3)

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