Question

What point divides the directed line segment ​ AB¯¯¯¯¯ ​ ⁢ into a 3:4 ratio? (4,​ 3) (7,​ 3) (9,​ 3) (12,​ 3) Segment A B in the coordinate plane with endpoint A at 1 comma 3 and endpoint B at 15 comma 3.

Answer 1

(7,​ 3)

Explanation:

Given that:

• point A( x₁ , y₁) ≡ (1 ,3)
• point B( x₂ , y₂) ≡ (15, 3)

Let point P (a, b) divides the directed line segment ​ AB¯¯¯¯¯ ​ ⁢ into a 3:4 ratio

So we have:

`P(a,b)=[a=(m\cdot x_2+n\cdot x_1)/(m+n),b=(m\cdot y_2+n\cdot y_1)/(m+n)]` , where m : n = 3 : 4

Let A(1 ,3) =
`(x_1,y_1), (15,3)=(x_2,y_2), m=3\text{ and }n=4.`

Upon substituting coordinates of our given points in section formula we will get:

`P(a,b)=[a=(3\cdot 15+4\cdot 1)/(3+4),b=(3\cdot 3+4\cdot 3)/(3+4)]`

P(a, b) = (a = 7, b = 3)

Hope it will find you well.

Answer 2

Therefore, the coordinates of point P(x ,y) are P ( 7 , 3 ) which divides the directed line segment AB into 3 : 4.Step-by-step explanation:

Given:

point A( x₁ , y₁) ≡ ( 0 ,-5)

point B( x₂ , y₂) ≡ (2 , 0)

Let point p( x , y ) divide Line AB in the ratio 3 : 4 i.e m : n

To Find:

P ( x, y ) = ?

Solution:

if point P( x , y) divide segment AB internally in the ratio m : n then the X coordinate and the Y coordinate is given by section formula:

`x=((mx_(2) +nx_(1)) )/((m+n))\\ \\and\\\\y=((my_(2) +ny_(1)) )/((m+n))\\\\`

On substituting the above given values in section formula we get

`x=((3* 15 +4* 1) )/((3+4))\\ \\and\\\\y=((3* 3 +4* 3))/((3+4))\\\\\\x=(49)/(7)=7\\\\and\\\\y=(21)/(7)=3\\`

Therefore, the coordinates of point P(x ,y) are P ( 7 , 3 ) which divides the directed line segment AB into 3 : 4.