9. The line segment $AB$ has the endpoints $A(2,-3)$ and $B(-4,-9)$. Point $C$ partitions the line at a ratio of $2:1$. What are the coordinates of point $C$ ?
$(-1,-10)$
$(-2,-7)$
$(4,1)$
$(-3,0)$

Step 1 ：Given the line segment $AB$ with endpoints $A(2,-3)$ and $B(-4,-9)$, and a point $C$ that partitions the line at a ratio of $2:1$.

Step 2 ：The coordinates of a point that divides a line segment in a given ratio can be found using the section formula. The section formula in vector form is given by: $$C=\frac{mB+nA}{m+n}$$ where m:n is the given ratio, A and B are the endpoints of the line segment, and C is the point that divides the line segment in the given ratio.

Step 3 ：Substitute the given values into the section formula: A = (2, -3), B = (-4, -9), and the ratio is 2:1.

Step 4 ：Calculate the coordinates of point C: C = (-2.0, -7.0)

Step 5 ：Final Answer: The coordinates of point C that divides the line segment AB in the ratio 2:1 are $\boxed{{\displaystyle (-2,-7)}}$.