Surveying I– coordinate account

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The length of the segment coordinate

Figure 1. The length of side AB of the coordinate system XY

The length of the section between points A and B can be easily calculated knowing the coordinates of two points. First, we determine northing and easting difference:

Δx = X_B – X_A, Δy = Y_B – Y_A

Then, using the formula:

D_AB = √_________ Δx² + Δy²

obtain the distance between points A and B.

Calculate the length of control can be made from one of the formulas:

D_AB = ΙΔxΙ cosφ


D_AB = ΙΔyΙ sinφ

where φ = arctg Δy Δx (the angle between the side AB and the direction of the north).

Example

alculate the distance between points A and B with the data of their coordinates.

Data:
A ( 137,63m; 367,78m)
B ( 189,60m; 942,58m)

SOLUTION

Δx = X_B – X_A = 51,97m
Δy = Y_B – Y_A = 574,80m


D_AB = √________ Δx² + Δy²


D_AB = √________________ 51,97² + 574,80²


D_AB = 577,14m

Control

φ = arctg Δy Δx


φ = arctg 574,80 51,97


φ = 94^g,25967


D_AB = ΙΔxΙ cosφ


D_AB = Ι51,97Ι cos(94^g,25967)


D_AB = 577,14m