If
O
N
=
8
x
−
8
,
L
M
=
7
x
+
4
,
N
M
=
x
−
5
,
and
O
L
=
3
y
−
6
,
find the values of x and y for which LMNO must be a parallelogram.
In a parallelogram, opposite sides are equal in length. Therefore, we can set up two equations:
ON = LM
8x - 8 = 7x + 4
x = 12
OL = MN
3y - 6 = 12 - 5
3y = 11
y = 11/3
Therefore, the values of x and y for which LMNO must be a parallelogram are x = 12 and y = 11/3.