Problem 7.4. In triangle $ABC$, the median $CM$ and the bisector $BL$ were drawn. Then, all segments and points were erased from the drawing, except for points $A(2 ; 8)$, $M(4 ; 11)$, and $L(6 ; 6)$. What were the coordinates of point $C$?

![](https://cdn.mathpix.com/cropped/2024_05_06_d4986512fdb0330805a0g-20.jpg?height=501&width=517&top_left_y=674&top_left_x=468)
Answer: $(14 ; 2)$.

Solution. Since $M$ is the midpoint of $A B$, point $B$ has coordinates (6;14). Since $\angle A B L=\angle C B L$, point $C$ lies on the line symmetric to line $A M$ with respect to the vertical line $B L$. Also, point $C$ lies on line $A L$. Carefully finding the intersection point of these lines "by grid", we get that $C$ has coordinates $(14 ; 2)$.

![](https://cdn.mathpix.com/cropped/2024_05_06_d4986512fdb0330805a0g-21.jpg?height=500&width=517&top_left_y=89&top_left_x=468)