Traverse balancing – quadrant of the closing error from sign of latitude and departure sums In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. In which quadrant will the closing line (resultant closing error) lie?

Introduction / Context:
In coordinate (latitude–departure) computations for traverses, the algebraic sums of latitudes (northings/southings) and departures (eastings/westings) diagnose misclosure. Their signs directly reveal the quadrant in which the closing error vector lies. This question tests your ability to infer that quadrant correctly from the given inequalities.

Given Data / Assumptions:

• ΣS > ΣN, so the net latitude is southing.
• ΣE > ΣW, so the net departure is easting.
• The resultant closing line is drawn from the computed end point back to the start point.

Concept / Approach:

Latitude is the north–south component; departure is the east–west component. If the algebraic sum indicates net southing and net easting, the closing error vector must point toward the south–east direction. Therefore, the closing line lies in the south–east quadrant (SE). After identifying the quadrant, balancing (e.g., Bowditch or transit rule) distributes corrections proportionally to remove the misclosure.

Step-by-Step Solution:

Verification / Alternative check:

Plot a simple vector with components (east positive, south negative). The directional quadrant immediately shows as SE, confirming the verbal reasoning.

Why Other Options Are Wrong:

NE requires net northing and easting; NW requires northing and westing; SW requires southing and westing. None match the given sign pattern.

Common Pitfalls:

Mixing signs for latitude and departure; drawing the closing line in the opposite sense; forgetting that ΣLat and ΣDep are computed algebraically with sign conventions.

Final Answer:

South–east quadrant