Question

consider the rotation of figure wxyz shown. complete the statements about the transformation shown. point w corresponds to point y . angle zwx corresponds to angle dropdown options: x yxw, yzw, zwx, zyx

Explanation:

Step1: Analyze Corresponding Angles in Rotation

In a rotation, corresponding angles are formed by the same set of corresponding vertices. For angle \( \angle ZWX \), the vertices are \( Z \), \( W \), \( X \). After rotation, the corresponding vertices should map \( Z \to Z' \), \( W \to Y' \) (given), \( X \to X' \)? Wait, no, let's check the figure. Wait, the original figure is \( WXYZ \), and the rotated figure is \( Y'X'W'Z' \)? Wait, no, let's look at the markings. The original figure has sides: \( ZW \) with two ticks, \( WX \) with two ticks? Wait, no, the original figure \( WXYZ \): \( ZW \) (two ticks), \( WX \) (two ticks? No, the rotated figure \( Y'X'W'Z' \): \( Y'X' \) has three ticks, \( X'W' \) has three ticks? Wait, the original figure \( WXYZ \): \( YX \) has three ticks, \( XW \) has two ticks? Wait, maybe the correspondence is \( W \to Y' \), \( X \to X' \), \( Y \to W' \), \( Z \to Z' \)? Wait, no, the angle \( \angle ZWX \) is at \( W \), between \( ZW \) and \( WX \). After rotation, the angle at \( Y' \) (since \( W \) corresponds to \( Y' \)) between the corresponding sides. The sides corresponding to \( ZW \) and \( WX \): \( ZW \) (two ticks) should correspond to \( Z'Y' \) (two ticks? Wait, the rotated figure \( Y'X'W'Z' \): \( Y'Z' \) has two ticks? Wait, no, let's check the angle markings. The original angle \( \angle ZWX \) has a certain arc marking, and the rotated angle should have the same arc marking. Looking at the options: \( \angle Z'Y'X' \): vertices \( Z' \), \( Y' \), \( X' \). Let's see: \( Z \to Z' \), \( W \to Y' \), \( X \to X' \). So \( \angle ZWX \) (vertices \( Z, W, X \)) corresponds to \( \angle Z'Y'X' \) (vertices \( Z', Y', X' \)), since \( Z \to Z' \), \( W \to Y' \), \( X \to X' \).

Step2: Verify the Correspondence

In a rotation, the order of the vertices in the angle should be preserved. So \( \angle ZWX \) (Z - W - X) should correspond to \( \angle Z'Y'X' \) (Z' - Y' - X'), because \( W \) maps to \( Y' \), \( Z \) maps to \( Z' \), \( X \) maps to \( X' \). So the angle \( \angle ZWX \) corresponds to \( \angle Z'Y'X' \).

Answer:

\( Z'Y'X' \)