Answer:
Step-by-step explanation:
The mid-segment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.
The two non-parallel sides of ABCD are BC and AD.
Midpoint of BC = (6, 6)
Midpoint of AD = (2, 4)
Therefore, length between midpoints [tex]=\sqrt{(6-2)^2+(6-4)^2} =2\sqrt{5} [/tex]
Gradient of mid-segment = [tex]\frac{6-4}{6-2}=\frac{1}{2} [/tex]
Using equation of a straight line and one of the midpoints:
[tex]y-y_1=m(x-x_1)\\
y-6=\frac{1}{2} (x-6)\\
y=\frac{1}{2} x+3[/tex]
So the equation of the line containing the mid-segment is [tex]y=\frac{1}{2} x+3[/tex]
