Question

rectangle wxyz is reflected over yz to create quadrilateral efgh. which statement must be true? a wx is parallel to zg. b points f and y are the same point. c the lengths of wy and hy are equal. d points w, z, and f all lie on the same line.

Explanation:

Step1: Recall reflection properties

When a rectangle is reflected over a line, corresponding points are equidistant from the line of reflection. In a rectangle, opposite sides are parallel. When rectangle WXYZ is reflected over YZ, W corresponds to E, X corresponds to F, Y corresponds to Y (on the line of reflection), and Z corresponds to Z (on the line of reflection). WX and ZY are opposite - sides of the rectangle WXYZ. After reflection, the side corresponding to WX will be parallel to the side corresponding to ZY. Since ZY is parallel to WX in the original rectangle, and reflection is a rigid transformation that preserves parallelism, WX is parallel to ZG (assuming G is the corresponding point of some other vertex related to the reflection).

Step2: Analyze other options

• Option A: Points F and Y being the same point is not a necessary property of a reflection over YZ.
• Option B: The lengths of WY and FY being equal is not a property that must hold for a reflection over YZ.
• Option C: Points W, Z, and F lying on the same line is not a necessary condition for the reflection of rectangle WXYZ over YZ.

Answer:

WX is parallel to ZG.