Answer
$M_1=\sqrt {37} ; M_2=\frac{\sqrt {145}}{2} ; M_3=\frac{\sqrt {109}}{2}$
Work Step by Step
M(AB) = $(\frac{3+1}{2};\frac{6+0}{2})$ = (2;3) = E
d(EC) = $\sqrt {(8-2)^2 + (2-3)^2} = \sqrt {6^2 + 1^2} = \sqrt {37}$
M(BC) = $(\frac{3+8}{2};\frac{2+6}{2})$ = ($\frac{11}{2};4$) = F
d(FA) = $\sqrt {(1-\frac{11}{2})^2 + (0-4)^2} = \sqrt {(-\frac{9}{2})^2 + (-4)^2} = \frac{\sqrt {145}}{2}$
M(AC) = $(\frac{1+8}{2};\frac{0+2}{2})$ = ($\frac{9}{2};1$) = G
d(GB) = $\sqrt {(3-\frac{9}{2})^2 + (
6-1)^2} = \sqrt {(-\frac{3}{2})^2 + (5)^2} = \frac{\sqrt {109}}{2}$
