Using Properties of Perpendicular Lines

First we draw an arc with center at point $P$ that intersects $\ell$ at two points, $A$ and $B.$

Next, we will draw two intersecting arcs. The arcs will have the same radius and one has its center in $A$ and the other its center in $B.$

Finally, we draw a line through $P$ and $Q.$

The line we just drew is perpendicular to line $\ell .$