Answer:
The co-ordinate of C is (0,-4).
Step-by-step explanation:
Given that , points A, B and C are collinear.
If all points lie in a same line, then the points are called co-linear.
The ratio AB to AC is 1:3.
It means the point A divided the line BC in ratio 1:3 externally.
The co-ordinate of A is (-2,-3) and the co-ordinate of B is (-6,-1).
If a line joining by two points (x₁,y₁) and (x₂,y₂) is divided by a point in the ratio m:n externally, then the co-ordinate of the point is
[tex](\frac {mx_2-nx_1}{m-n},\frac {my_2-ny_1}{m-n})[/tex]
Here x₁= -2,y₁= -3, x₂= -6,y₂= -1 and m=1 and n = 3
The co-ordinate of C is
[tex](\frac{1.(-6)-3(-2)}{1-3},\frac{1.(-1)-3(-3)}{1-3})[/tex]
[tex]=(\frac{-6+6}{-2},\frac{-1+9}{-2})[/tex]
[tex]=(0,\frac{8}{-2})[/tex]
=(0,-4)
