Question

in parallelogram lmno, mp = 21 m, lp = (y + 3) m, np = (3y - 1) m, and qp = (2x - 1) m. what are the values of x and y? x = 10 m, y = 1 m x = 10 m, y = 2 m x = 11 m, y = 1 m x = 11 m, y = 2 m

Explanation:

Step1: Use the property of parallelogram diagonals bisecting each other

In a parallelogram, the diagonals bisect each other. So, \(LP = NP\) and \(MP=OP\).
For \(LP = NP\):
\(y + 3=3y - 1\)

Step2: Solve the equation for \(y\)

Subtract \(y\) from both sides:
\(y+3 - y=3y - 1 - y\)
\(3 = 2y-1\)
Add \(1\) to both sides:
\(3 + 1=2y-1 + 1\)
\(4 = 2y\)
Divide both sides by \(2\):
\(y=\frac{4}{2}=2\)

Step3: Use \(MP = OP\) to find \(x\)

Since \(MP = 21\) and \(OP=(2x - 1)\), then \(2x-1 = 21\)
Add \(1\) to both sides:
\(2x-1 + 1=21 + 1\)
\(2x=22\)
Divide both sides by \(2\):
\(x=\frac{22}{2}=11\)

Answer:

\(x = 11\mathrm{m},y = 2\mathrm{m}\) (the fourth option)