40. Segment $\overline{A B}$ with endpoints at points $A(-3 ; 2)$ and $B(4 ;-5)$ is divided by point $C$ in the ratio $\lambda=-3$. Find the coordinates of the point of division.

![](https://cdn.mathpix.com/cropped/2024_05_22_1b9a1c1720bae4af5bc5g-018.jpg?height=372&width=484&top_left_y=656&top_left_x=59)

Fig. 8
Solution. Using formula (1), we get:

$$
\begin{aligned}
& x=\frac{-3+(-3) \cdot 4}{1+(-3)}=7.5 \\
& y=\frac{2+(-3)(-5)}{1+(-3)}=-8.5
\end{aligned}
$$

Thus, the desired point $C(7.5$; $-8.5$) divides the segment $\overline{A B}$ externally in the ratio $\frac{A C}{C B}=$ $=\lambda=-3$ (Fig. 8). Note that the lengths $A C$ and $C B$ have opposite signs.