18. The line segment $A B$ has the endpoints $(-10,15)$ and $(4,-6)$. Pont $C$ partitions the line at a ratio of $3: 4$ What are the coordinates of point $C$ ? The coordinates are given by $(x, y)$ where $x=$ , and $y=$

Step 1 ：The line segment $A B$ has the endpoints $(-10,15)$ and $(4,-6)$. Point $C$ partitions the line at a ratio of $3: 4$. We are asked to find the coordinates of point $C$.

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 states that if a point P(x, y) divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P are given by: \[x = \frac{m*x2 + n*x1}{m + n}\] and \[y = \frac{m*y2 + n*y1}{m + n}\]

Step 3 ：In this case, point C divides the line segment AB in the ratio 3:4. So, we can substitute the given values into the section formula to find the coordinates of point C.

Step 4 ：Substituting the given values into the formula, we get: \[x = \frac{3*(-10) + 4*4}{3 + 4} = -4.0\] and \[y = \frac{3*15 + 4*(-6)}{3 + 4} = 6.0\]

Step 5 ：Final Answer: The coordinates of point C are \(\boxed{(-4, 6)}\)