HELPPP!! 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 Correct Answer and Explanation is:
For LMNO to be a parallelogram, opposite sides must be equal in length. The opposite sides of the parallelogram in this case are:
- LM and ON
- NM and OL
So, we can equate the expressions for these pairs of opposite sides to find the values of xxx and yyy.
Step 1: Equate opposite sides
- LM = ON
From the given information, 7x+4=8x−87x + 4 = 8x – 87x+4=8x−8 Now, solve for xxx: 7x+4=8x−87x + 4 = 8x – 87x+4=8x−8 Subtract 7x7x7x from both sides: 4=x−84 = x – 84=x−8 Add 8 to both sides: x=12x = 12x=12 - NM = OL
From the given information, x−5=3y−6x – 5 = 3y – 6x−5=3y−6 Substitute x=12x = 12x=12 into this equation: 12−5=3y−612 – 5 = 3y – 612−5=3y−6 Simplify: 7=3y−67 = 3y – 67=3y−6 Add 6 to both sides: 13=3y13 = 3y13=3y Divide both sides by 3: y=133y = \frac{13}{3}y=313
Final Answer:
The values of xxx and yyy are:
- x=12x = 12x=12
- y=133y = \frac{13}{3}y=313
Thus, for LMNO to be a parallelogram, xxx must be 12 and yyy must be 133\frac{13}{3}313.
