Question

determine o comprimrnto da mediana AM do triangulo cujos vertices sãp A(2,3) B(4,-2) e C(0 e -6) ,em seguida calcule as coordenadas do baricentro

Answer 1

Primeiro achamos o ponto médio de BC

B(4,-2) e C(0,-6)

Xm = ( xb + xc ) / 2

Xm = ( 4 + 0 ) / 2

Xm = 4/2 = 2

Ym = ( yb + yc ) / 2

Ym = ( -2 - 6 ) / 2

Ym = -8/2 = -4

M(2,-4)

Agora calculamos a distância AM

A(2,3) e M(2,-4)

D² = ( xm - xa )² + ( ym - ya )²

D² = ( 2 - 2 )² + ( -4 - 3 )²

D² = ( -7 )²

D² = 49

D = √49

D = 7

Calcular as coordenadas do baricentro

XG = ( xa + xb + xc ) / 3

YG = ( ya + yb + yc ) / 3

XG = ( 2 + 4 + 0 ) / 3

XG = 6/3 = 2

YG = ( 3 - 2 - 6 ) / 3

YG = -5/3

G(2,-5/3)