Laurine Denesik
Jan 21, 2025
If ON= 8x-8, LM= 7x-4, NM= x-9 and OL= 5y-7, find the values of x and y for which LMNO must be a parallelogram.?
Given the equations ON = 8x - 8, LM = 7x - 4, NM = x - 9, and OL = 5y - 7, determine the values of x and y that will ensure that the quadrilateral LMNO is a parallelogram.
2 Answers
To be a parallelogram, both pairs of opposite sides must be equal in length, i.e. LM=ON and LO=MN
LM=ON
7x-4=8x-8 (-7x)
-4=x-8 (+8)
4=x
x=4
LO=MN
5y-7=x-9 (sub x=4)
5y-7=4-9
5y-7=-5 (+7)
5y=2 (/5)
y=2/5
Therefore,
x=4
y=2/5
opposite sides are congruent...did you make a diagram ? do it now !
You have BAD information in your problem !
ON = LM
8x - 8 = 7x - 4
solving for x gives: x = 4
However, if x = 4, then NM (which you say is (x - 9)) would be NEGATIVE...
CAN NOT HAVE A NEGATIVE DIMENSION !
Check your problem, check your post...repost the problem correctly !
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