Answer:
The equation for the median from vertex C is

Step-by-step explanation:
we know that
The <u><em>median</em></u> of a triangle is a line segment joining a vertex to the midpoint of the opposite side
In this problem
Is a line segment joining vertex C to the midpoint segment DE
step 1
Find the midpoint segment DE
we have
D (-2,2) and E (3,1)
The formula to calculate the midpoint between two points is equal to

substitute the given values


step 2
Determine equation of the median
The median passes through the points
C(1,4) and M(0.5,1.5)
Find the slope
The formula to calculate the slope between two points is equal to

substitute the values



Find the equation in point slope form

we have

substitute

Convert to slope intercept form
Isolate the variable y

therefore
The equation for the median from vertex C is
