if ON= 2x-7, LM= 4x+3, NM= x+6, and OL= 8y-7, find the values of x and y for which LMNO must be a parallelogram

Question

i need help with my topics in geometry homework

Answer 1

Hi John,

 

My guess is that there's a typo in your question:

 

     ON = 2x - 7

     LM = 4y + 3

     NM = x + 6

     OL = 8y - 7

 

Using these expressions, you'll find a valid solution for x and y, using the method Stephen suggested earlier.

 

Remember: the opposite sides of a parallelogram are parallel to each other and have equal length.

 

So, this means that ON = LM, and NM = OL:

 

     2x - 7 = 4y + 3

 

     x + 6 = 8y - 7

 

Here we have a system of two equations with two unknowns x and y. Solve for the unknowns using any method you like.

 

Best of luck!

Answer 2

The key requirement for a parallelogram is that the opposite sides need to have equal length.  Therefore,

 

ON = LM    and     NM = OL

2x-7 = 4x+3      x+6 = 8y-7

 

The first equation allows us to solve directly for x, so that's the most efficient place to start.  Subtracting 3 and 2x from each side, we get

 

-10 = 2x

-5 = x

 

That said, substituting gives a length for ON and LM of -17, which doesn't make a whole lot of sense.  I assume you have modified the problem for academic honesty (which I encourage).  Hopefully my answer gives you the framework to solve the actual problem in front of you.  In a typical problem, both equations that result will involve both x and y.  If that were the case, we can first solve one of the equations for one of the variables.  So if we take the second equation and subtract 6 from both sides, we get:

 

x = 8y-13

 

We could then substitute this into the other equation everywhere 'x' appeared and then solve for 'y'.

 

If you need any clarification, let me know.

Answer 3

Please describe the figure what are the letters starting from bottom left corner and reading clockwise because I'm getting x equals negative 5 and that does not make sense