2024 AMC 12B Problems/Problem 15
Problem
A triangle in the coordinate plane has vertices ,
, and
. What is the area of
?
Solution 1 (Shoelace Theorem)
We rewrite:
.
From here we setup Shoelace Theorem and obtain:
.
Following log properties and simplifying gives (B).
~MendenhallIsBald
Solution 2 (Determinant)
To calculate the area of a triangle formed by three points
The coordinates are:,
,
Taking a numerical value into account:
Simplify:
Thus, the area is: =
~Athmyx