2024 AMC 12B Problems/Problem 15
Contents
[hide]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 .
~MendenhallIsBald
Solution 2 (Determinant)
To calculate the area of a triangle formed by three points
Taking a numerical value into account: Simplify: Thus, the area is: =
Video Solution 1 by SpreadTheMathLove
https://www.youtube.com/watch?v=jyupN3dT2yY&t=0s
See also
2024 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.