<s>[INST] Median BM of triangle ABC two results Given


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*Calculate the measure of the median $\overline{BM}$ of ABC triangle, given A (-6.1); B (-5,7) and C (2,5)


I get this result:
$Xm = \frac{Xc - Xa}{2} + Xa$ 
$Xm = \frac{2-(-6)}{2} + (-6) = 4 - 6 = -2$
$Ym = \frac{(Yc - Ya)}{2} + Ya$
$Ym = \frac{5-1}{2} + 1 = 2 + 1 = 3$
$M(-2, 3)$
$d_{BM}^2 = (-5-(-2))^2 + (7-3)^2 = 9 + 16 = \sqrt{25} = 5$
and someone else get:
$Xm = \frac{-5+2}{2} = \frac{-3}{2}$
$Ym = \frac{7+5}{2} = \frac{12}{2} = 6$
$...$
So what's correct ?
 [/INST] First, both you and someone else seem to be using $B(-5,7)$, not $B(5,7)$. 
The "someone else" appears to be computing the midpoint between some other point $B(-5,7)$ and $C(2,5)$, and you are computing the midpoint between $A(-6,1)$ and $C(2,5)$. 
If you are really trying to compute the length $BM$ where $M$ is the midpoint of $AC$, the side opposite to $B$, then your answer is correct.
We don't have the complete "someone else" answer, so it is unclear what distance that person is computing, but the $M$ that person is computed is the midpoint of $BC$, not the midpoint of $AC$.
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