19. Given points $A(3 ; 4)$ and $B(6 ; 6)$. On the $O y$ axis, determine the point $C$ such that the area of triangle $A B C$ is equal to 5.
Solution. Let's form the column, noting that $C(0 ; y)$ :

![](https://cdn.mathpix.com/cropped/2024_05_21_b1a79769c6c63d19f37fg-17.jpg?height=206&width=223&top_left_y=899&top_left_x=928)

From this, $F_{3}=-3 y+6$. Since $S_{3}=5$, then $\frac{1}{2}|-3 y+6|=5$, from which $y_{1}=-1 \frac{1}{3}, y_{2}=5 \frac{1}{3}$.

Therefore, the problem has two solutions: $C_{1}\left(0 ;-1 \frac{1}{3}\right)$ and $C_{2}\left(0 ; 5 \frac{1}{3}\right)$.