We're supposed to calculate average acceleration:

 

So we're given a situation of a plane traveling some distance with four different velocities. We were taught that, to draw a velocity vector diagram for it (NOT a displacement one), we're supposed to use draw it using the first and last given velocities. Then, say we know an angle for the triangle formed, we can use cosine law to find the resultant displacement.

 

My question is, since acceleration is a = Δv/Δt, then why do we need to find the resultant displacement, why not just subtract v2 from v1 to find the change in velocity? Why use the displacement?

You can subtract v2 from v1. That's Δv. But, you also need Δt. You can either use the graph, or divide by t1 subtracted from t2. But, you definitely cannot just ignore Δt.