Question

Considere os pontos A(1,-2), B(2,0) e c(0,-1). O comprimento da mediana triângulo ABC, relativa ao lado AC, é:

Answer 1

Ponto médio de AC M(AC):
 $x=1+ \frac{0}{2} = \frac{1}{2} y=-2- \frac{1}{2}  = \frac{-3}{2}$

BM:
B(2, 0)
$M( \frac{1}{2} , \frac{-3}{2} )$
$BM^{2} = (-2 \frac{-1}{2}) ^{2} + (0+ \frac{3}{2}) ^{2}$
$B M^{2}=( \frac{3}{2})^2+( \frac{3}{2})^2$
$BM^{2} = \frac{9}{4}+ \frac{9}{4}$
$BM^2= \frac{18}{4}$
$BM= \frac{\sqrt{18} }{\sqrt{4} }= \frac{\sqrt{9}. 2}{2} = \frac{3\sqrt{2} }{2}$