Question

1. in parallelogram pqrs, if diagonal pr is bisected at point o and po = 3x + 4, while or = 5x - 2, what is the value of x?

o a. 2
o b. 3
o c. 4
o d. 1

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, diagonals bisect each other. So \( PO = OR \).

Step2: Set up equation

Given \( PO = 3x + 4 \) and \( OR = 5x - 2 \), set them equal: \( 3x + 4 = 5x - 2 \).

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 4 = 2x - 2 \).
Add 2 to both sides: \( 6 = 2x \).
Divide by 2: \( x = 3 \).

Answer:

b. 3