Question

find the ratio in which the line 2x+y=4 divide the join of A(2,-2)B(3,7) also find the cordinates of the point of there intersection

Answer 1

Let

P

(

x

,

y

)

be the point of intersection of the line

2

x

+

y

=

4

and the line joining

A

(

2

,

−

2

)

and

B

(

3

,

1

)

,

Assume that

P

divides line segment

A

B

in the ration of

1

:

n

,

By section formula,

P

(

x

,

y

)

=

(

1

×

3

+

n

×

2

1

+

n

,

1

×

1

+

n

(

−

2

)

1

+

n

)

=

(

3

+

2

n

1

+

n

,

1

−

2

n

1

+

n

)

Substituting

P

(

x

,

y

)

in

2

x

+

y

−

4

=

0

,

2

⋅

(

3

+

2

n

)

1

+

n

+

1

−

2

n

1

+

n

−

4

=

0

⇒

6

+

4

n

1

+

n

+

1

−

2

n

1

+

n

=

4

⇒

7

+

2

n

=

4

+

4

n

⇒

2

n

=

7

−

4

⇒

n

=

3

2

Hence, the ratio is

2

:

3