Respuesta :
Answer:
The coordinates of the point on the directed line segment from (-4, - 7) to
(-3,1) that partitions the segment into a ratio of 2 to 3 is
[tex]\therefore P(x,y)=(\frac{-18}{5},\frac{-19}{5})[/tex]
or
∴ PointP( x , y ) = ( -3.6, -3.8)
Step-by-step explanation:
Let he points be,
point A( x₁ , y₁) ≡ ( -4 ,-7)
point B( x₂ , y₂) ≡ (-3 , 1)
and Point P( x , y ) be the point on the line Segment AB Divides AB internally in the ratio 2 : 3 i. e m : n
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
[tex]x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}\\\\[/tex]
Substituting the Given values we get
[tex]x=\frac{(2(-3) +3(-4)) }{(2+3)}\\ \\and\\\\y=\frac{(2(1) +3(-7)) }{(2+3)}\\\\x=\frac{-18}{5}\\ \\and\\\\y=\frac{-19}{5}\\\\\therefore P(x,y)=(\frac{-18}{5},\frac{-19}{5})[/tex]
∴ PointP( x , y ) = ( -3.6, -3.8)
