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Let P and Q be the reference points on the ground. You have to establish a point R. Which of the following methods conforms to the fundamental principles of surveying?
Only I
Only III
I, II and III
Only I and II
I, II and III
The fundamental principle of surveying is to work from the whole to the part and to locate a new point with respect to at least two established reference points. All three methods illustrated (trilateration/triangulation in I, perpendicular offset in II, and intersection/triangulation using angles in III) provide sufficient geometric constraints to fix the location of point R relative to points P and Q.
The fundamental principle of surveying is to work from the whole to the part and to locate a new point with respect to at least two established reference points. All three methods illustrated (trilateration/triangulation in I, perpendicular offset in II, and intersection/triangulation using angles in III) provide sufficient geometric constraints to fix the location of point R relative to points P and Q.
d=(xRтАЛтИТxPтАЛ)2+(yRтАЛтИТyPтАЛ)2тАЛ тАФ distance formula for coordinate geometry
R=P+LтЛЕn тАФ vector-based point establishment
In surveying, to uniquely fix a point R in a 2D plane, two independent linear or angular measurements from two known control points P and Q are required. Method I uses linear distances PR and QR (trilateration). Method II uses a linear distance QS and a right-angle perpendicular offset SR. Method III uses two known internal angles ╬▒ and ╬▓ from the baseline PQ (triangulation/intersection).
Establishing a point requires at least two independent measurements from reference stations.
Method I relies on side-lengths (PR,QR).
Method II relies on an offset distance (SR) at a fixed orientation (perpendicular).
Method III relies on angular measurements (╬▒,╬▓) to the baseline (PQ).
Redundancy is preferred, but these methods represent the primary geometric minimums for position fixing.
Methods are standard practice in plane surveying.
Geometric derivation ensures high accuracy in locating points.
Independent measurement methods allow for cross-checking.
Requires clear lines of sight or distance access.
Susceptible to instrumental errors in angle measurement.
Detail plotting in chain surveying.
Tacheometry and triangulation networks.
Offset measurement for road and boundary surveys.
The core requirement of surveying is 'to work from the whole to the part' to prevent error accumulation, and all these methods adhere to basic geometric rules for establishing control points.
Method I is standard in trilateration. Method II is standard for detailing objects (offsets). Method III is standard in triangulation.
C is correct тАФ all three methods (I, II, and III) correctly illustrate standard geometric principles for fixing a new point R relative to two established control points P and Q.
Always remember that in surveying, the number of independent measurements must at least equal the number of unknowns to fix a point's position.
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