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,
![Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})](https://tex.z-dn.net/?f=Mid%5C%20point%28AC%29%3D%28%5Cdfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%20%7D%7B2%7D%2C%20%5Cdfrac%7By_%7B1%7D%2By_%7B2%7D%20%7D%7B2%7D%29)
Substituting the values we get
![B(2,0)=(\dfrac{0+x_{2} }{2}, \dfrac{-9+y_{2} }{2})](https://tex.z-dn.net/?f=B%282%2C0%29%3D%28%5Cdfrac%7B0%2Bx_%7B2%7D%20%7D%7B2%7D%2C%20%5Cdfrac%7B-9%2By_%7B2%7D%20%7D%7B2%7D%29)
Substituting x and y value we get
![2=\dfrac{0+x_{2} }{2}\\and\\0=\dfrac{-9+y_{2} }{2}](https://tex.z-dn.net/?f=2%3D%5Cdfrac%7B0%2Bx_%7B2%7D%20%7D%7B2%7D%5C%5Cand%5C%5C0%3D%5Cdfrac%7B-9%2By_%7B2%7D%20%7D%7B2%7D)
![x_{2}=4\\and\\y_{2}=9](https://tex.z-dn.net/?f=x_%7B2%7D%3D4%5C%5Cand%5C%5Cy_%7B2%7D%3D9)
Therefore the coordinates of C is
C(4,9).