SOLUTION: The vertices of a triangle are given below. Use a determinant and the vertices of the triangle to find the area of the triangle. (-3,-7.5), (-1.5,6.5), (1.5,-5.5) ** By the w

Algebra ->  Matrices-and-determiminant -> SOLUTION: The vertices of a triangle are given below. Use a determinant and the vertices of the triangle to find the area of the triangle. (-3,-7.5), (-1.5,6.5), (1.5,-5.5) ** By the w      Log On


   

Question 431116: The vertices of a triangle are given below. Use a determinant and the vertices of the triangle to find the area of the triangle.
(-3,-7.5), (-1.5,6.5), (1.5,-5.5)
** By the way: I know that the answer is 30, I just don't understand how to get the answer. Thank you
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have Area+=+%281%2F2%29%28abs%28det%28A%29%29%29 where A =
| -3 -7.5 1 |
| -1.5 6.5 1 |
| 1.5 -5.5 1 | (3x3 matrix)

Here,

det%28A%29+=+-36+-+22.5+-+1.5+=+-60, abs%28det%28A%29%29+=+60

Therefore, the area is equal to 1/2 of 60, or 30.