The diagram shows a quadrilateral WXYZ.

1. Construct equal-radius arcs from the endpoints of $XY$ and draw the bisector line.

Set the compass radius to more than half of $XY$.

With centre $X$, draw arcs above and below $XY$. Using the same radius and centre $Y$, draw arcs above and below $XY$ to intersect the first pair of arcs.

Join the two arc-intersection points with a straight line. This line is the perpendicular bisector of $XY$.

1. Construct the angle bisector of $angle WXY$.

With centre $X$, draw an arc cutting $XW$ and $XY$ at two points. Using the same radius from these two points, draw two arcs meeting inside angle WXY. Draw a straight line from $X$ through the intersection of the arcs. This line is the bisector of angle WXY.

1. Identify the required region and mark a valid point $A$.

Since $A$ is equidistant from $X$ and $Y$, $A$ must lie on the perpendicular bisector of $XY$.

Since $A$ is closer to line $WX$ than to line $XY$, choose the point on the side of the angle bisector of $\angle WXY$ nearer to $WX$, not the side nearer to $XY$.

Therefore, mark and label any point $A$ inside the quadrilateral on the perpendicular bisector of $XY$ and on the $WX$ side of the angle bisector.