Geometry

Question Analysis:
This is a multi-step algebraic geometry question involving two pairs of segments (parts of diagonals).
The main focus is on using the property that diagonals in a parallelogram bisect each other, meaning:
WO = OY
XO = OZ

Key Concept Explanation:
If a quadrilateral is a parallelogram, then both diagonals must be bisected by their point of intersection.
That gives us two equations to solve — the values of WO and OY must be equal, and likewise for XO and OZ.

Step-by-Step Solution:
Step 1: Set up equations based on the bisection property.
WO = OY → 3x − 2 = x + 4
XO = OZ → 2x + 1 = 4x − 5
Step 2: Solve each equation separately.
Equation 1: 3x − 2 = x + 4 → 2x = 6 → x = 3
Equation 2: 2x + 1 = 4x − 5 → −2x = −6 → x = 3

Common Mistakes:
Solving only one equation instead of checki...