How can I Programmatically Determine the Trigger Time and Sample Point for a Set Record Length on the DL850/DL750 ScopeCorder?

To determine the exact trigger time of the waveform acquisition, use the ":HISTORY:TIME? 0" command, where 0 refers to the latest acquisition record.
To determine the exact trigger sample number, use the ":WAVEFORM:TRIGGER?" command. The number of samples that would be read from the scope is:

                        No. of Points = Record Length * 1.001

Since the trigger sample number is counted from the first point, you can ignore the last 0.1% of the record length. For example, if the record length is 10k points, the total sample points must be 10,000 *1.001 = 10,010 points. You can ignore the last 10 points, 10,000*0.001 = 10 points.

The Time Zero can be counted from the first point.
Sample Rate(SR): ':WAVEFORM:SRATE?'
Trigger Position(TP): ' :WAVEFORM:TRIGGER?'
The Time Zero is at this Trigger Point.
So the relative time of the first point of the wavefrom data is SR*TP*(-1).
 
Please refer to the attached image file of the DL850 ScopeCorder Manual Instruction Manual IMDL850-01EM Chapter 3, for more information on how the total number of sample points is calculated.