can someone help me please I'm doing this for math Olympics

A contractor is asked to build a new set of townhouses in attached clusters of


different sizes. He created plans for one-, two-, and three-house clusters, as shown in the diagram below. The builder used computer software to draw the line segments used to represent the houses. How many line segments are needed to draw 4 houses? 10 houses? 47 houses? n houses? Explain your strategy.