Question Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. If ON = 8x − 8, LM = 7x + 4, NM = x − 5, and OL = 3y − 6, find the values of x and y for which LMNO must be a parallelogram. (2 points)
In a parallelogram, opposite sides are equal in length.
So, we can set up the following equation:
ON = LM and NM = OL
8x - 8 = 7x + 4 and x - 5 = 3y - 6
To solve the first equation:
8x - 7x = 4 + 8
x = 12
To solve the second equation:
x - 5 = 3y - 6
x - 3y = -1
12 - 3y = -1
-3y = -13
y = 13/3
Therefore, x = 12 and y = 13/3 for LMNO to be a parallelogram.