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 exact area is:
\[\boxed{\text{B. \log_2 \frac{3}{\sqrt{7}}}}\] (Error compiling LaTeX. Unknown error_msg)
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