Question

calcule o comprimento das medianas de um triangulo de vertices A(-4,6) , B(8,2) e C(0,10)

Answer 1

Boa tarde Flah

mediana relativa ao vértice C

Mx = (Ax + Bx)/2 = (-4 + 8)/2 = 4/2 = 2
My = (Ay + By)/2 = (6 + 2)/2 = 8/2 = 4 

dCM² = (Cx - Mx)² + (Cy - My)² 
dCM² = (0 - 2)² + (10 - 4)²
dCM² = 4 + 36 = 40
CM = 2√10 

mediana relativa ao vértice B

Mx = (Ax + Cx)/2 = (-4 + 0)/2 = -4/2 = -2
My = (Ay + Cy)/2 = (6 + 10)/2 = 16/2 = 8

dBM² = (Bx - Mx)² + (By - My)² 
dBM² = (8 + 2)² + (2 - 8)²
dBM² = 100 + 36 = 136
BM = 2√34 

mediana relativa ao vértice A

Mx = (Bx + Cx)/2 = (8 + 0)/2 = 8/2 = 4
My = (By + Cy)/2 = (2 + 10)/2 = 12/2 = 6

dAM² = (Ax - Mx)² + (Ay - My)² 
dAM² = (-4 - 4)² + (6 - 6)²
dAM² = 64
AM = 8