Graphing the same point twice

Question

If I'm graphing the same point twice does the name change? For example, if I had to go from $A (7,10)$ to $B (8,11)$ to $C (6,4)$ and I was writing down the coordinates and their names so that someone else could copy my figure, would I put $A (7,10)$ or $D (7,10)$ and write $D$ near $A$ on the coordinate plane to close the figure.

Answer 1

Two ways you can do this:

you can name each distinct point uniquely and then have a list of the waypoints for your path, like

$$\begin{align}A &= (7,10)\\B &= (8,11)\\C &= (6,4)\end{align}$$ and then your path is $A,B,C,A$

Or, you can just have a list of the waypoints without real consideration for the name: $(7,10), (8,11),(6,4),(7,10)$.

The former has advantages when you have several paths that go through the same waypoints; the latter works better when you're unlikely to repeat waypoints.