1. The lines containing the sides of a certain quadrilateral are given by the equations $\mathrm{y}=\mathrm{ax}+\mathrm{b}$, $\mathrm{y}=\mathrm{ax}+\mathrm{c}, \quad \mathrm{y}=\mathrm{dx}+\mathrm{b}, \quad \mathrm{y}=\mathrm{dx}+\mathrm{c}$. Find the coordinates of the point of intersection of the diagonals of the considered quadrilateral.
Solution. Obviously, the quadrilateral is a parallelogram. Two opposite vertices of it (corresponding to the intersections of the pairs of lines $\mathrm{y}=\mathrm{ax}+\mathrm{b}, \mathrm{y}=\mathrm{dx}+\mathrm{b}$ and $\mathrm{y}=\mathrm{ax}+\mathrm{c}, \mathrm{y}=\mathrm{dx}+\mathrm{c}$) have coordinates (o,b) and (o,c), respectively. The point of intersection of the diagonals of the parallelogram is located at the midpoint of this diagonal and has coordinates (o, (b+c)/2).