How do you find the area of a triangle plot as point A = (-2,5); B = (12,3); C = (10,-11)?

1 Answer
Gió
Jul 9, 2015

I found #100# units of area

Explanation:

There may be different ways to solve this but I thought of one that is quite intriguing:
Area=#+-1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|#
i.e. #1/2# times the determinant formed using your coordinates and a column of #1# (the #+-# is to "correct" possible negative values).
So, in your case:
Area=#+-1/2|(-2,5,1),(12,3,1),(10,-11,1)|=+-1/2(-200)=100# u.a.
"correcting" the minus sign.

The demonstration and reference of the above method can be found in:

Ron Larson - Elementary Linear Algebra 7th ed. 2013

Related questions
See all questions in Area of a Triangle
Impact of this question
2913 views around the world
You can reuse this answer
Creative Commons License