Talk:2020 AMC 10B Problems/Problem 8

Solution 3 (Imagination)

We can draw out line $PQ$ and see that $PQ$ must either be the base or the height of the right triangle. We can now split this problem in 2 cases.

Case 1: $PQ$ is the height. We can have point 2 on each side of $Q$ and each side of $P$ . Which leads to $4$ cases.

Case 2: $PQ$ is the base. We can see that R can be a point below $P$ or above and the same for $Q$ Which again leads to $4$ cases.

$4+4=\boxed{\textbf{(D)}\ 8}$ locations for $R.$

~Ic3paw