33. The line segment $A B$ has the endpoints $A(7,-16)$ and $B(-8,-4)$. Point $C$ partitions the line at a ratio of $2: 1$. What are the coordinates of point $C$ ?

Step 1 ：Given the endpoints of the line segment AB as A(7,-16) and B(-8,-4), and the ratio in which point C partitions the line as 2:1.

Step 2 ：We can find the coordinates of point C using the section formula in vector form: \(C = \frac{mB + nA}{m + n}\), 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 ：Substituting the given values into the section formula, we get: A = (7, -16), B = (-8, -4), and the ratio is 2:1.

Step 4 ：Calculating the coordinates of point C, we get C = (-3.0, -8.0).

Step 5 ：Thus, the coordinates of point C that divides the line segment AB in the ratio 2:1 are (-3.0, -8.0).

Step 6 ：Final Answer: The coordinates of point C are \(\boxed{(-3.0, -8.0)}\).