The equations of the three lines must be considered in pairs to find the coordinates of their points of intersection, i.e. the coordinates of the vertices of the triangle. By solving each pair of simultaneous equations, you should find that the coordinates are $(-15,-9)$, $(0,6)$ and $(5,1)$. The area of the triangle may now be found by enclosing the triangle in a rectangle and subtracting the areas of the three surrounding triangles from the area of the rectangle. This gives $300 - (112½ + 12½ + 100) = 75$.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*

View the current weekly problem