Answer
$AM_{BC}=\sqrt{36.25}$
$BM_{AC}=\sqrt{27.25}$
$CM_{AB}=\sqrt{37}$
Work Step by Step
To find lengths of the medians we first have to find coordinates of the midpoints and then we will calculate the lengths using distance formula.
According to the Midpoint formula, for $A(x_1,y_1)$, $B(x_2,y_2)$: $M=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
We have sides, $AB$, $BC$, $AC$
$M_{AB}=(\frac{1+3}{2}, \frac{0+6}{2})=(2, 3)$
$M_{BC}=(\frac{3+8}{2}, \frac{6+2}{2})=(5.5, 4)$
$M_{AC}=(\frac{1+8}{2}, \frac{0+2}{2})=(4.5, 1)$
Next, we will calculate distance of the medians, using distance formula:
$AM_{BC}=\sqrt{(5.5-1)^2+(4-0)^2}=\sqrt{20.25+16}=\sqrt{36.25}$
$BM_{AC}=\sqrt{(4.5-3)^2+(1-6)^2}=\sqrt{2.25+25}=\sqrt{27.25}$
$CM_{AB}=\sqrt{(2-8)^2+(3-2)^2}=\sqrt{36+1}=\sqrt{37}$
