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brendacauani12345
29.01.2020 •
Mathematics
Surveying crew located three points on a map that formed the vertices of a triangular area. a coordinate grid in which on unit equals 20 miles is place over the map so that the vertices are located at (0, -1), (-3, -9), and (3, -2). find the area of the triangle using determinants?
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Ответ:
5400 mi²
Step-by-step explanation:
The area is half the absolute value of the sum of the determinants of the points taken pairwise in some consistent order around the polygon. For a triangle, this sum of determinants can also be written as the determinant of a 3×3 matrix of the coordinates with the third column being 1.
... Area = (1/2)|D|
where D = ...
Then the area is (in grid squares) ...
... Area = (1/2)|27| = 13.5 . . . . grid squares
Each grid square is (20 mi)² = 400 mi², so 13.5 grid squares is ...
... 13.5 × 400 mi² = 5400 mi²
Ответ: