Question

Determine as coordenadas do Baricentro (G) dos triângulos com vértices:

a) Δ ABC: A(2, 3), B(5, -1) e C(-1, 4)
b) Δ DEF: D(-1, 0), E(2, -3) e F(2, 3)
c) Δ HIJ: H(-1, -4), I(7, 6) e J(6, 1)
d) Δ KLM: K(-2, 5), L(3, 2) e M(5, -7)
Obs: Pessoal quem puder me ajudar agradeço!

Answer 1

a) Δ ABC: G (2, 2)

$Xg = \frac{xA + xB + xC}{3} \\ \\ Xg = \frac{2 + 5 + (-1)}{3} \\ \\ Xg = \frac{6}{3} \\ \\ Xg = 2\\ \\ \\ Yg = \frac{yA + yB + yC}{3} \\ \\ Yg = \frac{3 + (-1) + 4}{3} \\ \\ Yg = \frac{6}{3} \\ \\ Yg = 2$

G (2, 2) ← Baricentro do triângulo ABC
__________

b) Δ DEF: G (1, 0)

$Xg = \frac{xA + xB + xC}{3} \\ \\ Xg = \frac{- 1 + 2 + 2}{3} \\ \\ Xg = \frac{3}{3} \\ \\ Xg = 1\\ \\ \\ Yg = \frac{yA + yB + yC}{3} \\ \\ Yg = \frac{0 + (-3) + 3}{3} \\ \\ Yg = \frac{0}{3} \\ \\ Yg = 0$

G (1, 0) ← Baricentro do triângulo DEF
__________

c) Δ HIJ: G (4, 1)

$Xg = \frac{xA + xB + xC}{3} \\ \\ Xg = \frac{-1 + 7 + 6}{3} \\ \\ Xg = \frac{12}{3} \\ \\ Xg = 4\\ \\ \\ Yg = \frac{yA + yB + yC}{3} \\ \\ Yg = \frac{-4 + 6 + 1}{3} \\ \\ Yg = \frac{3}{3} \\ \\ Yg = 1$

G (4, 1) ← Baricentro do triângulo HIJ
__________

d) Δ KLM: G (2, 0)

$Xg = \frac{xA + xB + xC}{3} \\ \\ Xg = \frac{-2 + 3 + 5}{3} \\ \\ Xg = \frac{6}{3} \\ \\ Xg = 2\\ \\ \\ Yg = \frac{yA + yB + yC}{3} \\ \\ Yg = \frac{5 + 2 + (-7)}{3} \\ \\ Yg = \frac{0}{3} \\ \\ Yg = 0$

G (2, 0) ← Baricentro do triângulo KLM