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A(0,4)b(2,2) and c(-2,-1) Which expression represents the perimeter of the triangle​

A(0,4)b(2,2) and c(-2,-1) Which expression represents the perimeter of the triangle-example-1

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2 votes

Answer:

Option B

Explanation:


Distance = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}

A(0,4) & B(2,2)


AB =\sqrt{(2-0)^(2)+(2-4)^(2)}\\\\=\sqrt{2^(2)+(-2)^(2)}\\\\=√(4+4)\\\\=√(8)\\\\=√(2*2*2)\\\\=2√(2)\\

B(2,2) & C(-2,-1)


BC =\sqrt{(-2-2)^(2)+(-1-2)^(2)}\\\\=\sqrt{(-4)^(2)+(-3)^(2)}\\\\=√(16+9)\\\\=√(25)\\\\=√(5*5)\\\\=5

A(0,4) ; C(-2,-1)


AC=\sqrt{(-2-0)^(2)+(-1-4)^(2)}\\\\=\sqrt{(-2)^(2)+(-5)^(2)}\\\\=√(4+25)\\\\= √(29)

Perimeter of triangle = AB + BC + AC


= 5 +2√(2)+√(29)

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