Question

use the figure shown for items 4–5.

if xz = 7x + 1 and pz = 4x − 1, what is xp?

a. 11

b. 12

c. 19

d. 22

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, diagonals bisect each other. So \( XP = PZ \) and \( XZ = XP + PZ = 2 \times PZ \).

Step2: Set up equation using the property

Given \( XZ = 7x + 1 \) and \( PZ = 4x - 1 \), and \( XZ = 2 \times PZ \), so:
\( 7x + 1 = 2(4x - 1) \)

Step3: Solve for \( x \)

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

Step4: Find \( PZ \) then \( XP \)

Since \( XP = PZ \), substitute \( x = 3 \) into \( PZ = 4x - 1 \):
\( PZ = 4(3) - 1 = 12 - 1 = 11 \)
So \( XP = 11 \)

Answer:

A. 11