Answer:
Therefore,
[tex]P(x,y)=(2,10)[/tex]
Step-by-step 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
[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{(3\times 5 +1\times -7) }{(3+1)} \ \ \ and\ \ \ y=\dfrac{(3\times 12 +1\times 4) }{(3+1)}\\\\\\\therefore x = \dfrac{8}{4}=2 \ \ and\ \ \therefore y = \dfrac{40}{4}=10\\\\\\\therefore P(x,y) = (2 , 10)[/tex]
Therefore,
[tex]P(x,y)=(2,10)[/tex]
