Answer:
The equation for the median from vertex C is
[tex]y=5x-1[/tex]
Step-by-step explanation:
we know that
The median 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
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the given values
[tex]M(\frac{-2+3}{2},\frac{2+1}{2})[/tex]
[tex]M (0.5,1.5)[/tex]
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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{1.5-4}{0.5-1}[/tex]
[tex]m=\frac{-2.5}{-0.5}[/tex]
[tex]m=5[/tex]
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=5\\C(1,4)[/tex]
substitute
[tex]y-4=5(x-1)[/tex]
Convert to slope intercept form
Isolate the variable y
[tex]y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
therefore
The equation for the median from vertex C is
[tex]y=5x-1[/tex]
