Measure the width of the room in two places and in each case mark its exact center on the floor.
Snap a wall-to-wall chalk line lined up on the marks.
Measure the chalk line and mark its center to indicate the room's center point.
Line up a framing square along the chalk line at the center point, then make a line along the square's tongue perpendicular to the chalk line. Do the same on the other side of the chalk line.
Snap a second wall-to-wall chalk line on the perpendicular lines to divide the room into quadrants (as shown).