Since LMNO is a square, the midpoint of the diagonal LN can be found with the midpoints of sides LM and MN.
To find the 'x' coordinate of the midpoint, we find the 'x' coordinate of the midpoint of side LM:
[tex]L(-6,1),M(1,1),N(1,8)[/tex]
To find the 'x' coordinate we substract the 'x' coordinates from L to M:
[tex]1-(-6)=7[/tex]
Then divide by two and substract from 'x' coordinate of M:
[tex]1-\frac{7}{2}=-\frac{5}{2}[/tex]
We do something similar to find the 'y' coordinate. Substract y coordinate of M from y coordinate of N:
[tex]8-1=7[/tex]
Divide by 2 and add the 'y' coordinate of M:
[tex]1+\frac{7}{2}=\frac{9}{2}[/tex]
Then, the coordinates of the midpoint of diagonal LN are:
[tex](-\frac{5}{2},\frac{9}{2})[/tex]
