7. Find the point $C$ that divides the segment between points $A(-1)$ and $B(5)$ in the ratio:
1) $\lambda=\frac{2}{3}$; 2) $\lambda=-2$.
Solution. Applying formula (3), we find the coordinate of point $C$:

1) $x=\frac{-1+\frac{2}{3} \cdot 5}{1+\frac{2}{3}}=1.4$
2) $x=\frac{-1+(-2) \cdot 5}{1+(-2)}=11$.

Thus: 1) $C(1.4)$; 2) $C(11)$.