Question

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

Answer 1

Answer:

Option B

Step-by-step explanation:

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

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

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

B(2,2)  & C(-2,-1)

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

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

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

Perimeter of triangle = AB + BC + AC

                                  $= 5 +2\sqrt{2}+\sqrt{29}$