Find the orthocentre of the triangle with vertices (0, 0), (6, 0) and (4, 4).

The altitude from (4, 4) to the $x$-axis is the line $x=4$. The side from (6, 0) to (4, 4) has slope −2, so the altitude from the origin has slope $\frac{1}{2}:y=\frac{x}{2}$. They meet at (4, 2).