Answer
$A: 0,0 \\ B: a,b \\ C: 2a,0$
Work Step by Step
An ideally placed triangle, which we will call triangle ABC, should have point A placed at the origin and side AC be on the x-axis. Calling the length of AC "2a" and the height "b," we obtain:
$A: 0,0 \\ B: a,b \\ C: 2a,0$