# Which is the length of the median from the vertex A(1,3) of triangle ABC? B(-3,1), C(3,-3)

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To calculate the length of a segment, we have to know the coordinates of the endpoints of the segment.

In this case, we know the coordinates of the A endpoint, which is a vertex of the triangle ABC.

But we know that the segment whose length we have to calculate is the median in the triangle ABC. That means that the other endpoint is the midpoint of the side BC.

xM = (xB+xC)/2

xM = (-3+3)/2

xM = 0

yM = (yB+yC)/2

yM = (1-3)/2

yM = -1

The coordinates of the midpoint M(0,-1).

Now, we could calculate the length of AM:

AM = sqrt [(xM-xA)^2 + (yM-yA)^2]

AM = sqrt [(0-1)^2 + (-1-3)^2]

AM = sqrt(1+16)

**AM = sqrt17**

Median is the distance from A(13) to the mid point of B(-3,1) and C(3,-3),

Mid point D of BC has coordinates : ((Bx +Cy)/2 , (By+Cy)/2) = ((-3+3)/2 , (1-3)/2) = (0,-1).

AD = sqrt[(Ax*Dx)^2+(Ay-Dy)^2] = sqrt[(1-0)^2+(3--1)^2] = sqrt(1+4) =sqrt5.