3. The points of intersection of the graphs of four functions given by the formulas $y=k x+b, y=k x-b, y=m x+b$ and $y=$ $m x-b$ are the vertices of a quadrilateral. Find the coordinates of the point of intersection of its diagonals.
Answer: $(0 ; 0)$.

Solution. The graphs of the given linear functions are two pairs of parallel lines, since the slopes of the first and second lines and the slopes of the third and fourth lines are equal. Therefore, the points of intersection of the graphs are the vertices of a parallelogram. Two opposite vertices of this parallelogram are $M(0 ; b)$ and $N(0 ;-b)$. Since the diagonals of a parallelogram bisect each other at the point of intersection, the required point is the midpoint of segment $M N$, that is, the point ( $0 ; 0$ ).

Grading criteria.

“+" - a complete and justified solution is provided

“ $\pm$ " - a generally correct reasoning is provided, containing minor gaps or inaccuracies

“耳” - only the correct answer is provided

“-" - the problem is not solved or is solved incorrectly