# absolute_data.txt
# X   Y
1   2
2   3
3   2
4   1

Fig. 1 Plotting absolute data points. (code to produce this figure, data)

This can be plotted in a straightforward manner and will result in Fig. 1. Now suppose we have the same data points stored as relative coordinates in our data file, resulting in:

# relative_data.txt
# deltaX deltaY
1   2
1   1
1   -1
1   -1

If we want to plot that data in gnuplot we have to keep track of the current position manually by storing its (x,y) value as variables by

x=0.; y=0.
plot 'relative_data.txt' u (x=x+$1):(y=y+$2) w p ls 1

Here, we define the starting point to be (0,0) and add to it the values from the first and second column for every line of the data file. By doing so, this results again in Fig. 1. Note, that the addition is always performed first, before the resulting point is plotted which means we get no point at (0,0). Now assume that we also want to add steps going from point to point as shown in Fig. 2. Gnuplot has the steps plotting style to achieve this, but we have to be carefully regarding our (x,y) variables.

Fig. 2 Plotting relative data points. (code to produce this figure, data)

Every single line of a plotting command is executed after each other which means our (x,y) pair will not be set to (0,0), but to (4,1) at the beginning of the second line of the plotting command. To avoid this we introduce another (a,b) pair for the second line and get finally.

x=0.; y=0.
a=0.; b=0.
plot 'relative_data.txt' u (x=x+$1):(y=y+$2) w steps ls 2,\
     ''                  u (a=a+$1):(b=b+$2) w points ls 1

# x   y
1   2

But there exist an easier method without any additional data file. In Fig. 1 three points with different symbols are plotted.

Fig. 1 Plot of three single points (code to produce this figure)

To achieve this we just use the following command:

plot '-' w p ls 1, '-' w p ls 2, '-' w p ls 3
1 2
e
2 1
e
3 1.5
e

We use the possibility to tell Gnuplot with the '-' input to read from standard input. Here we tell Gnuplot to do this three times. After the plot command the data is entered. Every single data entry have to ended with the e line.
In order to have different symbols for the points we set them before:

set style line 1 lc rgb 'black' pt 5   # square
set style line 2 lc rgb 'black' pt 7   # circle
set style line 3 lc rgb 'black' pt 9   # triangle

Note: if we want to use the replot command then the above code will not work probably. But the same can be achieved by using:

plot "<echo '1 2'"   with points ls 1, \
     "<echo '2 1'"   with points ls 2, \
     "<echo '3 1.5'" with points ls 3