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Someone just robbed a bank. The police set a triangular perimeter of 16 kilometers where the robber may be hiding. Two of the three
coordinates for this triangular perimeter are (2, 2) and (2, -1). Each unit represents a kilometer. The area covered is a 12 square kilometers
Which of the following is the third coordinate of the triangular perimeter?

Respuesta :

Answer:

Step-by-step explanation:

Perimeter = 16 km

s = 8 km

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Area = 12 sq km

Let the third coordinate be (x,y).

Then, a = [tex]\sqrt{(2-2)^{2}+(2-(-1))^{2}  }[/tex]

=3

b =  [tex]\sqrt{(x-2)^{2}+(y-2)^{2}  }[/tex]

c =  [tex]\sqrt{(x-2)^{2}+(y-(-1))^{2}  }[/tex]

Solving, a+b+c = 16

and using area equation we get

x = -6

y = 2

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