Understanding Point Establishment in Surveying

In surveying, establishing a new point means determining its precise location relative to other known points. This is a fundamental task in setting out construction works, mapping, or creating control networks. The accuracy of the established point depends heavily on the reliability of the reference points used.

The Role of Reference Points in Surveying

Reference points are locations whose coordinates (horizontal and/or vertical) are already known and assumed to be fixed or stable. These points form the basis of a surveying network. To establish a new point, surveyors measure angles, distances, or both, from one or more of these known reference points to the new point.

Why At Least Two Fixed Points Are Needed

Consider the process of locating a point on a 2D plane. If you only have one reference point, you can determine the distance from it to the new point. This defines a circle around the reference point where the new point could lie, but doesn't give a unique location.

If you have two reference points, you can use methods like:

• Intersection: Measuring angles from each reference point to the new point. The intersection of the lines defined by these angles gives the unique location.
• Trilateration: Measuring distances from each reference point to the new point. The intersection of the circles defined by these distances gives the unique location (though there might be two possible intersection points, which can usually be resolved based on the context).

Both these basic methods require measurements from at least two distinct reference points to uniquely determine the position of a new point in a 2D plane. For 3D positioning, similar principles apply, often involving height references as well.

Analyzing the Options

Let's look at the given options in the context of surveying principles:

• at the most three points of reference: There is no upper limit of three. Surveyors can and often do use more than three reference points for redundancy, error checking, and improving accuracy, especially in larger projects or control networks.
• at the most two, already fixed points of reference: This sets an upper limit of two, which is incorrect. More than two points are frequently used.
• at least two points of reference: This correctly states "at least two points" are needed. However, it misses a crucial detail: the reference points must be "already fixed" or known control points. Using arbitrary, unfixed points wouldn't allow you to determine the new point's location relative to a known system.
• at least two, already fixed points of reference: This option correctly identifies the minimum requirement ("at least two") and specifies that these reference points must be "already fixed," meaning their positions are known and reliable. This allows for the unique and accurate determination of the new point's position.

Conclusion

Based on the fundamental principles of surveying, establishing the position of a new point requires referencing it from locations whose coordinates are already known and stable. A minimum of two such fixed reference points is necessary to uniquely determine the location of the new point using common surveying techniques like intersection or trilateration.

Therefore, a point in surveying is established using at least two, already fixed points of reference.

Revision Table: Key Surveying Concepts

Additional Information: Surveying Networks

Surveying often involves creating a network of fixed points, called control points. These points are established with high accuracy using techniques like GPS, triangulation, trilateration, or traversing, often tied to national or global coordinate systems. When establishing a new point for a specific project, surveyors connect it to at least two of these existing, already fixed control points within the network. Using more than two points provides redundancy, which helps detect errors and improve the overall accuracy and reliability of the determined position of the new point.