Question

Dado a 2,6 b 4,2 e c -2,4 vértice do triângulo abc, detrmine a medida das medianas; AM BN CP?

Answer 1

Bom dia 

A(2,6), B(4,2), C(-2,4) 

ponto médio  M

Mx = (Bx + Cx)/2 = 1
My = (By + Cy)/2 = 3

mediana AM

dAM² = (Ax - Mx)² + (Ay - My)²
dAM² = 1² + 3² = 10 , AM = √10 

ponto médio  N

Nx = (Ax + Cx)/2 = 0
Ny = (Ay + Cy)/2 = 5

mediana BN

dBN² = (Bx - Nx)² + (By - Ny)²
dBN² = 4² + 3² = 25 , AM = 5 

ponto médio  P

Px = (Bx + Ax)/2 = 1
Py = (By + Ay)/2 = 3

mediana CP

dCP² = (Cx - Px)² + (Cy - Py)²
dCP² = 3² + 1² = 10 , CP = √10