=> 2y = x+k
=> y = x/2+k/2
comparing with y = mx+c
m(slope) = 1/2
This equation represents a random median on the triangle, and to find out which one we need to find the median whose slope is the same as this equation's.
Name midpoints of AB, BC and AC points M, N and O respectively.
Medians are AO, BN and CM
Let N coordinates be (a,b)
By midpoint theorem, N coordinates,
a = (-1-5)/2 = -3
b = (3+2)/2 = 5/2
slope formula = difference of y coordinates / difference of x coordinates
∴ slope (BN) = (4-(5/2))/(0-(-3)) = (8-5)/2(3) = 3/6 = 1/2
which is the same as the equation's slope.
Therefore, the equation provided is for median BN, this means that point B falls on the median.
Substituting B's coordinates in the given equation,
=> (0)-2(4)+k = 0
=> -8+k = 0
=> k = 8