Question

A,B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1

Answer 1

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,

$Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})$

Substituting the values we get

$B(2,0)=(\dfrac{0+x_{2} }{2}, \dfrac{-9+y_{2} }{2})$

Substituting x and y value we get

$2=\dfrac{0+x_{2} }{2}\\and\\0=\dfrac{-9+y_{2} }{2}$

$x_{2}=4\\and\\y_{2}=9$

Therefore the coordinates of C is

C(4,9).