Question

if xz = 7x + 1 and pz = 4x - 1, what is xp?
a. 11
b. 12
c. 19
d. 22

Explanation:

Step1: Recall property of parallelogram

In parallelogram \(WXYZ\), the diagonals bisect each other. So \(XP = PZ\) and \(XZ=2PZ\).

Step2: Set up equation

Since \(XZ = 7x + 1\) and \(PZ=4x - 1\), and \(XZ = 2PZ\), we have the equation \(7x + 1=2(4x - 1)\).

Step3: Solve the equation

Expand the right - hand side: \(7x + 1 = 8x-2\).
Subtract \(7x\) from both sides: \(1=x - 2\).
Add 2 to both sides: \(x=3\).

Step4: Find the length of \(PZ\)

Substitute \(x = 3\) into the expression for \(PZ\): \(PZ=4x - 1=4\times3-1=12 - 1 = 11\).

Step5: Find the length of \(XP\)

Since \(XP = PZ\), then \(XP = 11\).

Answer:

A. 11