Question

Os pontos A (2,-4), B (-2,1) E C (4,5) São vértices de um triangulo. Determine o comprimento das mediadas do triangulo ABC e as coordenadas do baricentro.

Answer 1

b = baricentro

$b=(\frac{2-2+4}{3},\frac{-4+1+5}{3})\\\\b=(\frac{4}{3},\frac{2}{3})\\\\\=A\=B=\sqrt{(2-(-2)^2+(-4-1)^2}\\\\\=A\=B=\sqrt{4^2+(-5)^2}\\\\\=A\=B=\sqrt{16+25}\\\\\=A\=B=\sqrt{36}\\\\\=A\=B=6\\\\\=B\=C=\sqrt{(-2-4)^2+(1-5)^2}\\\\\=B\=C=\sqrt{(-6^2)+(-4)^2}\\\\\=B\=C=\sqrt{36+16}\\\\\=B\=C=\sqrt{52}\\\\\=C\=A=\sqrt{(4-2)^2+(-4-5)^2}\\\\\=B\=C=\sqrt{4+81}\\\\\=B\=C=\sqrt{85}$