2024 AMC 8

Solution 1

Since the triangle has a base of , we can plug in that value as the base. Then, we can solve the equation for the height. Doing so gives us,

This means that , so that means that we have to add 4 to the -coordinate. So the answer is

Solution 2

By the Shoelace Theorem, has area

From the problem, this is equal to . We now solve for y.

OR

OR

OR

However, since, as stated in the problem, , our only valid solution is .