4. Example
A crew surveyed the exterior of the parcel shown. They assumed the coordinates of the southernmost corner (1001) and used the record bearing for the southwesterly line (10011002).


Figure H20 Parcel Survey 
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 H21 Drainfield Survey 
When the coordinates were brought together and plotted the results were as shwon in Figure H22:
Figure H22 Parcel and Drainfield Combined 
Using the boundary survey as the reference system, translate the drainfield data.
Determine transformation parameters
Step (1) Rotation angle
Line NENW coincides with line 10031002; line NENW must be rotated into line 10031002.
Convert the bearings to azimuths and compute the rotation angle.
Line NENW  
Line 10001002 
From Equation H1:
Step (2) Scale
Length of line NENW is 476.41', line 10031002 is 476.37'.
From Equation H2:
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 (3) Translations
Use the coordinates of points 1003 and NE in Equation H3:
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:
Step (5) Transform points 501504
Use Equation H14 with the parameters computed in Steps (1)(3)
Point 501
Point 502
Point 503
Point 504