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:
=
See also
2024 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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All AMC 12 Problems and Solutions |
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