Answer:
Therefore the coordinates of C is
C(4,9).
Step-by-step explanation:
Given:
Point A , B , and C are Collinear.
i.e A-B-C is a Straight Line
AB : BC = 1 : 1
i.e B is the Mid Point of AC.
And Point A , B and C lie on the Same Line
point A( x₁ , y₁) ≡ ( 0 ,-9)
point B( x , y) ≡ (2 , 0)
To Find:
point C( x₂ , y₂) ≡ ?
Solution:
B is the Mid Point of AC. Hence by Mid point Formula,
[tex]Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})[/tex]
Substituting the values we get
[tex]B(2,0)=(\dfrac{0+x_{2} }{2}, \dfrac{-9+y_{2} }{2})[/tex]
Substituting x and y value we get
[tex]2=\dfrac{0+x_{2} }{2}\\and\\0=\dfrac{-9+y_{2} }{2}[/tex]
[tex]x_{2}=4\\and\\y_{2}=9[/tex]
Therefore the coordinates of C is
C(4,9).
