Median of a triangle? Math question!

the centroid G of a triangle has coordinates which are the average of the coordinates of the triangle vertices

here
xG = (6 + 12 +6)/3 = 8
yG = (8 + 4 - 6)/3 = 2

G (8, 2)

If you want to find median equation from X, you need coordinates of the midpoint M of YZ
which are the average of the coordinates of Y and Z, so M (9, -1)
Then you find the equation of the line XM
4x - y = 30

the same from Z
3x + y = 26

then you solve the system of the equations of the two medians

4x - y = 30
3x + y = 26

add the right sides and the left sides
7x = 56
x = 8

substitute in the second equation
24 + y = 26
y=2

Draw the figure.
We have X (6, 8), Y (12, 4) and Z ( 6, - 6)
Let A be the mid point of YZ. Coordinates of A are given by A (9, - 1)
Slope of the median XA = m1 = (8 + 1) / (6 - 9) = - 3
The median XA passes through X (6, 8).
Its equation is : y - 8 = - 3(x - 6)
=> y = - 3x + 26 ........ (1)
Let C be the mid-point of XY. Coordinates of C are given by C ( 9, 6)
Slope of the median ZC = m3 = (- 6 - 6) / (6 - 9) = 4
The median ZC passes through Z(6, - 6)
Its equation is : y + 6 = 4(x - 6)
=> y = 4x - 30 ...... (2)
Let the point of intersection of the medians XA and ZC be the Centroid G(m, n)
From (1) and (2), we get
n = - 3m + 26 and n = 4m - 30
=> - 3m + 26 = 4m - 30
=> 7m = 56
=> m = 8
=> n = 2
Hence, Centroid G (m, n) = (8, 2)

IT IS SO EASY
FIRST U FIND THE SLOPE OF THE LINE (XZ) AND THEN USE POINT SLOPE FORMULA TO FIND THE EQUATION OF THE LINE(XZ)
AND THE CENTROID IS 1/3 OF THE MEDIAN'S LENGTH , SO U FIND THE LENGTH OF THE SAME SEGMENT XZ AND THEN DIVIDE BY 3 U WILL GET THE CENTROID