Answer:
Therefore the coordinates of the point on the directed line segment from (-2, 9) to (-1, -4) that partitions the segment into a ratio of 2 to 3 is
[tex]P(x,y)=(-\dfrac{8}{5},\dfrac{19}{5})[/tex]
Step-by-step explanation:
Given:
Let point P divides Segment AB in the ratio 2 : 3
point A( x₁ , y₁) ≡ ( -2 , 9 )
point B( x₂ , y₂) ≡ ( -1 , -4 )
m : n = 2 : 3
To Find:
P( x, y ) = ?
Solution:
Ia a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as
[tex]x=\dfrac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\dfrac{(my_{2} +ny_{1}) }{(m+n)}\\\\[/tex]
Substituting the values we get
[tex]x=\dfrac{(2(-1) +3(-2))}{(2+3)}\\ \\and\\\\y=\dfrac{(2(-4) +3(9)) }{(2+3)}\\\\[/tex]
[tex]x=\dfrac{-8}{5}\\ \\and\\\\y=\dfrac{19}{5}\\\\[/tex]
Therefore the coordinates of the point on the directed line segment from (-2, 9) to (-1, -4) that partitions the segment into a ratio of 2 to 3 is
[tex]P(x,y)=(-\dfrac{8}{5},\dfrac{19}{5})[/tex]
