Question

Sendo A, B e C os vértices de um triângulo e G o seu baricentro, determine o que se pede:

a) A(-5, -3), B(5, -1), G(2/3, 1/3), C= ?

b) A(1/2, -3/2), C(1, 5/2), G(4/3, 1/3), B= ?

Answer 1

G [ (xa+xb+xc)/3 , (ya+yb+yc)/3 ]

(A)

2/3 = (-5 + 5 + xc)/3

2/3 = xc/3

2*3 = 3xc

xc = 2

1/3 = (-3-1 + yc)/3

1/3 = (yc-4)/3

3 = 3*(yc-4)

yc-4 = 1

yc = 5

C (2,5)

(B)

4/3 = (1/2 + 1 + xb)/3

4 = 1/2 + 1 + xb

4 = 1/2 + 2/2 + xb

4 = 3/2 + xb

8/2 - 3/2 = xb

xb = 5/2

1/3 = (-3/2 + 5/2 + yb)/3

1 = -3/2 + 5/2 + yb

1 = 1 + yb

yb = 0

B (5/2,0)