We have to calculate the midpoint for each segment.
To do that we have to calculate the average for the coordinates of each point.
1) For AB, we have A = (-5,8) and B = (-5,6).
We can then calculate the midpoint coordinates as:
[tex]M_{AB}=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})=(\frac{-5+(-5)}{2},\frac{8+6}{2})=(-\frac{10}{2},\frac{14}{2})=(-5,7)[/tex]2) For BC we have B = (-5,6) and C = (-2,6).
The midpoint will be:
[tex]M_{BC}=(\frac{-5+(-2)}{2},\frac{6+6}{2})=(\frac{-7}{2},\frac{12}{2})=(-\frac{7}{2},6)[/tex]3) For CD we have C = (-2,6) and D = (2,3).
The midpoint will be:
[tex]M_{CD}=(\frac{-2+2}{2},\frac{6+3}{2})=(\frac{0}{2},\frac{9}{2})=(0,\frac{9}{2})[/tex]4) For DE we have D = (2,3) and E = (2,-1).
The midpoint will be:
[tex]M_{DE}=(\frac{2+2}{2},\frac{3+(-1)}{2})=(\frac{4}{2},\frac{2}{2})=(2,1)[/tex]5) For EF we have E = (2,-1) and F = (6,0).
The midpoint will be:
[tex]M_{EF}=(\frac{2+6}{2},\frac{-1+0}{2})=(\frac{8}{2},-\frac{1}{2})=(4,-\frac{1}{2})[/tex]Answer:
AB = (-5,7)
BC = (-7/2,6)
CD = (0,9/2)
DE = (2,1)
EF = (4,-1/2)