Final answer:
To find the third coordinate of the triangular perimeter, we can use the concept of area of a triangle. By using the given coordinates, the distance formula, and the equation of the line passing through the two given points, we can solve a system of equations to find the values of x and y.
Step-by-step explanation:
The third coordinate of the triangular perimeter can be found by using the concept of area of a triangle. We know that the area of the triangle is 12 square kilometers and the base of the triangle is the distance between the two given coordinates, which is 3 kilometers. Let's assume the third coordinate is (x, y). We can use the formula for the area of a triangle:
Area = (base * height) / 2
Substituting the known values, we get:
12 = (3 * height) / 2
Solving for height, we find:
height = 8 kilometers
Now, we can use the given coordinates to find the distance between them, which is the height of the triangle. Using the distance formula, we have:
height = sqrt((x-2)^2 + (y+1)^2)
Squaring both sides and rearranging the equation, we get:
(x-2)^2 + (y+1)^2 = 64
Since we have two unknowns, we need another equation to solve for x and y. Let's use the equation of the line passing through the two given points:
y - 2 = (2 - (-1)) / (2 - 2) * (x - 2)
Expanding and rearranging the equation, we get:
3x - y - 6 = 0
Now, we have a system of equations:
(x-2)^2 + (y+1)^2 = 64
3x - y - 6 = 0
Solving this system of equations will give us the values of x and y, which represent the third coordinate of the triangular perimeter.