The curve represented by the given figure is something curve.
And we have two possible choices. Is it a closed curve or an open curve? Let’s remind ourselves what these two terms mean, so that we know which one we can choose to fill the gap.
A closed curve is any line at all that has the same start and end points. In a way, it’s like taking a line for a walk and arriving back where we started. An open curve is any line at all that has different start and end points. So we start somewhere, we draw our line, and then we end up in a different place to where we started. So which of these two types of curve can we see here?
Let’s choose a starting point, follow the line, and see where it takes us. Let’s start here. As we follow the line, let’s remind ourselves what we’re looking for. If this is a closed curve, then we’ll end up back where we started, the same start and end points. If this is an open curve, then where we’ll end up will be different to where we started. It will have different start and end points.
And you see which of the two types of curve this is looking like it’s going to be. We end up back where we started. And so we know that this is a closed curve. And so we can say the curve represented by the given figure is a closed curve.