5. Numeric Example
A crew surveyed the exterior of a parcel, Figure J23. They assumed the coordinates of the southernmost corner (1001) and used the record bearing for the southwesterly line (10011002)
Figure J23 


Later, a second survey crew was sent out to locate the existing drainfield. They did not have the first crew's coordinates so they occupied the northernmost corner (NE), for which they assumed coordinates, and backsighted the westernmost corner (NW), for which they assumed a direction. They then shot the drainfield corners. As a check, they also shot the distance from NE to NW. Figure 24 is a summary of their survey.
Figure J24 
Assumed dir NENW: N 90°00'00" W 
The data was combined in a CAD drawing with the result shown in Figure J25.
Figure J25 
Using the boundary survey as the reference system, translate the drainfield data.
a. Determine transformation parameters
Step (1) Scale
Length of line NENW is 476.41', line 10031002 is 476.37'.
From Equation J1:
This represents a distortion of 1/(10.999916) = 1/11,900. If this is within tolerance, then the scale factor can be ignored. We will apply it in this example.
Step (1) Rotation angle
Line NENW coincides with line 10031002; Convert the bearings to azimuths and compute the rotation angle.
Line NENW  
Line 10031002  
Using Equation J2  
Step (3) Translations
Use the coordinates of points 1003 and NE in Equations J3 and J4 to determine the translations.
Step (4) Math check
For a parameters math check, convert NW to see if it matches the coordinates of 1002.
In the From system, NW's coordinates are:
Transform and check:
Yuo, it checks.
b. Using Equations J5 and J6 transform the drainfield corners: 501504
Point 501
Point 502
Point 503
Point 504