Trong mặt phẳng tọa độ oxy, cho đường thẳng d : 3x+y-9=0

Correct option is 7

Step-by-step explanation:

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

)=(1,3) and (x

2

,y

2

)=(2,7) in thesection formula, we get the point which divides as (

k+1

k(2)+1(1)

,

k+1

k(7)+1(3)

)=(

k+1

2k+1

,

k+1

7k+3

)

Since this point lies on the line 3x+y−9=0, we have

3(

k+1

2k+1

)+

k+1

7k+3

−9=0

=>6k+3+7k+3−9k−9=0

4k−3=0

k=

4

3

Hence, the ratio is a:b=3:4 internally.

So a+b=7

14

step-by-step explanation: