Question

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

Answer 1

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)`