# Clustering algorithm for a coordinate-based matrix

I have $$1000$$ scenarios, each of which is composed of $$5$$ users' coordinates $$(x_i,y_i), \forall i \in \{1,\dots,5\}$$. Now, based on users' coordinates, I want to cluster these $$1000$$ scenarios into 100 clusters. Specifically, if users in two scenarios keep proximal or same coordinates, such two scenarios should be grouped into the same cluster.

My idea is to create a matrix with $$1000$$ scenarios as rows and $$5$$ users' coordinates (i.e., $$5$$ x-coordinates and $$5$$ y-coordinates) as columns. The matrix will hence have $$1000$$ rows and $$10$$ columns. Then, I apply a clustering algorithm such as k-means to cluster these $$1000$$ scenarios into $$100$$ clusters.

My concern is how to define a distance or similarity metric based only on these coordinates. Can anyone help me with this? Any comments would be appreciated!