Question

20 POINTS

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.

Answer 1

To find x:

ON is parallel to LM

8x - 8 = 7x + 4

-7x -7x

1x - 8 = 4

+8 +8

1x = 12

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1 1

x = 12

8(12) - 8 = 7(12) + 4

96 - 8 = 84 + 4

88 = 88

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To find y:

NM is parallel to OL

x - 5 = 3y - 6

12 - 5 = 3y - 6

7 = 3y - 6

+6 +6

13 = 3y

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3 3

13/3 = y

Check:

12 - 5 = 3(13/3) - 6

7 = 13 - 6

7 = 7