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