This word problem is killing me. Help?

Question

A real estate agent is writing a listing for a triangular piece of land. She has to include the number of square feet for the property and has to calculate it from a plot that shows the following information: one corner of the plot is 128 feet south and 124 feet east from the upper vertex of the plot, the other corner is 20 feet south and 268 feet east from the upper vertex of the plot. Use matrices to find the area of the piece of land.

Answer 1

Let the upper vertex be the origin, and E/W and N/S be the standard directions for the x axis and y axis.

Then the other points are (-128,124) and (-20,268)

The area if the triangle formed by (0,0), (x,y) and (u,v) is:

|xv-yu|/2.

Or 1/2 the absolute value of the determinant of the matrix:

x y
u v

So in the above case:

| -128*268 - 124 *(-20)|/2

That's 15912 square feet.

Answer 2

Use the dimensions as (x,y) points, assuming the "upper vertex" is (0,0). Calculate the length of each side, then calc the area of the triangles. If you need further help, msg me.. I'm on for a bit.

Answer 3

Let one corner be at (0,0)
Then vertex is at (124,128)
So other corner is at (392,108)
That should give you the data to solve the problem.