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. The diagram is not drawn to scale.
ON = LM and NM = OL
Since ON = LM, we can set their expressions equal to each other:
8x - 8 = 7x + 4
Subtracting 7x from both sides:
x - 8 = 4
Adding 8 to both sides:
x = 12
Now, since NM = OL, we can set their expressions equal to each other:
x - 5 = 3y - 6
Adding 6 to both sides:
x + 1 = 3y
Substituting the value of x we found earlier, which is 12, into the equation:
12 + 1 = 3y
13 = 3y
Dividing both sides by 3:
y = 13/3
Therefore, when x = 12 and y = 13/3, LMNO must be a parallelogram.