SOLUTION: find the area of a triangle whose veritces are as follows: (2,3), (3,8), (6,-1). SHow the set up.

Algebra ->  Matrices-and-determiminant -> SOLUTION: find the area of a triangle whose veritces are as follows: (2,3), (3,8), (6,-1). SHow the set up.      Log On


   

Question 253662: find the area of a triangle whose veritces are as follows: (2,3), (3,8), (6,-1). SHow the set up.
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!





The area of a triangle with vertices (a,b), (c,d), and (e,f) is

Area=abs%28%281%2F2%29%2Aabs%28matrix%283%2C3%2Ca%2Cb%2C1%2Cc%2Cd%2C1%2Ce%2Cf%2C1%29%29%29

Area=abs%28%281%2F2%29%2Aabs%28matrix%283%2C3%2C2%2C3%2C1%2C3%2C8%2C1%2C6%2C-1%2C1%29%29%29

Do you know how to evaluate that determinant?  If not post again
asking how.

Area=abs%28%281%2F2%29%2A%28-24%29%29=abs%28-12%29=12

Note that if you take the vertices in counter-clockwise order around
the triangle, the absolute value bars are not necessary, because the
area will come out positive anyway and so sometimes the formula is 
given without the absolute value bars, and they tell you to always
take the vertices in counter-clockwise order; however if you include 
the absolute value bars, then it doesn't matter which order
you take the vertices.  Notice that I took them clock-wise above,
and the absolute value bars were necessary.


Edwin