Question

Given points A(-7, 4) and B(5, 12), find the point P that partitions directed line segment top enclose A B end enclose in the ratio of 3:1. Type your answer as an ordered pair (x,y).

Answer 1

Therefore,

`P(x,y)=(2,10)`

Explanation:

Given:

Let Point P ( x , y ) divides Segment AB in the ratio 3 : 1 = m : n (say)

point A( x₁ , y₁) ≡ ( -7 , 4)

point B( x₂ , y₂) ≡ (5 , 12)

To Find:

point P( x , y) ≡ ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

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

Substituting the values we get

`x=((3* 5 +1* -7) )/((3+1)) \ \ \ and\ \ \ y=((3* 12 +1* 4) )/((3+1))\\\\\\\therefore x = (8)/(4)=2 \ \ and\ \ \therefore y = (40)/(4)=10\\\\\\\therefore P(x,y) = (2 , 10)`

Therefore,

`P(x,y)=(2,10)`