Median of a triangle? Math question!

Hey guys i need a little help on this please!

The vertices of a triangle are X (6, 8), Y (12, 4), Z (6, -6). Find the equations of the medians from X and Z and then find the point of intersection of these two medians (the centroid).

A median bisects the line it meets.

So to find the median from X, we would need to find the midpoint of Y and Z.

Midpoint(YZ) = [(x1+x2)/2, (y1+y2)/2]
= [(12+6)/2, (4+-6)/2]
= (9, -1)

To find the median from Z, we need to find the midpoint of X and Y.
Midpoint(XY) = [(x1+x2)/2, (y1+y2)/2]
= [(6+12)/2, (8+4)/2]
= (9, 6)

Therefore the median from X is (9,-1), median from Z is (9,6)

Now to find the point of intersection, we need two lines.

The line of X to its median will need to be determined using a gradient and a point. We will be using the points median of X (9,-1) and X (6,8) to find the gradient.
Gradient = (y2-y1)/(x2-x1)
= (-1-8)/(9-6)
= -3
A point we will use is X (6,8)
Use the point gradient formula.
y - y1 = m(x-x1)
y - 8 = -3 (x-6)
y-8 = -3x +18
3x + y -26 = 0

Now we need to find the line of median Z (9,6) to Z (6,-6)
Gradient = (y2-y1)/(x2-x1)
= (6 - - 6)/(9-6)
= 4

Using the point of median of Z (9,6)
Use Point Gradient Formula
y - y1 = m(x-x1)
y - 6 = 4 (x - 9)
y-6 = 4x - 36
4x - y -30 = 0

So now we have two lines:
X to median from X : 3x + y -26 = 0
Z to median from Z : 4x - y -30 = 0

We must now solve simultaneously to find the point of intersection (I will be referring to it as P.O.I)

So here are our two equations.
3x + y -26 = 0 (1)
4x - y -30 = 0 (2)

From (1)
3x + y -26 = 0
y = -3x +26 (1A)

Sub (1A) into (2)
4x - y -30 = 0 (2)
4x - (-3x + 26) -30 = 0
4x +3x -26 -30 = 0
7x = 56
x = 8

sub x = 8 into (1A)
y = -3x +26
y = -3(8) + 26
y = 2

Therefore, P.O.I (8,2)