Plane table surveying — what is the typical accuracy of a 'fix' obtained by the two-point resection problem compared with the standard three-point method?

Introduction / Context:In plane table surveying, a 'fix' means determining the map position of an unknown instrument station by sighting known control points. The two-point problem uses only two known points to orient the table and obtain a fix, whereas the three-point problem uses three known points and is the standard, more stable method. This question asks about the accuracy and practical reliability of the two-point fix.

Given Data / Assumptions:

• Only two well-defined control points are visible from the unknown station.
• Orientation must be obtained graphically (or with auxiliary station) before plotting the fix.
• No redundant geometric check is available from a third ray.

Concept / Approach:

With only two rays, many configurations are ill-conditioned: small sighting or plotting errors rotate the table and shift the computed position noticeably along the line of intersection. The two-point problem therefore lacks the inherent redundancy and error trapping of the three-point problem. While auxiliary-station techniques can improve matters, the general guidance remains that the two-point fix is inferior in reliability and should be avoided when a third point is available.

Step-by-Step Solution:

Verification / Alternative check:

Textbook rules (e.g., Lehmann’s) emphasize the superiority of three-point resection for accuracy; two-point methods are reserved for constrained visibility or as preliminary orientation.

Why Other Options Are Wrong:

Good — overstates the accuracy; two-point lacks redundancy.Bad — ambiguous; 'not reliable' is the accepted characterization.Unique — false; geometry allows multiple near-fits due to rotation sensitivity.

Common Pitfalls:

Trusting a two-point fix without independent checks; ignoring poor geometry (points nearly collinear) which magnifies error.

Final Answer:

not reliable