Question

figure pqrs is reflected to form figure wxyz. which side of figure wxyz corresponds with qr? which angle of figure wxyz corresponds with ∠p? options for angle: ∠w, ∠x, ∠y, ∠z

Explanation:

First Sub - Question (Side Correspondence)

Step1: Analyze the reflection

Since figure \(PQRS\) is reflected to form \(WXYZ\), we need to find the corresponding side to \(QR\). Let's look at the vertices. In \(PQRS\), the sides are \(PQ\), \(QR\), \(RS\), \(SP\). In \(WXYZ\), the sides are \(WX\), \(XY\), \(YZ\), \(ZW\). By matching the order of vertices (since reflection preserves the order of vertices in a congruent figure), \(QR\) in \(PQRS\) (connecting \(Q\) to \(R\)) should correspond to \(XY\) in \(WXYZ\) (connecting \(X\) to \(Y\))? Wait, no, let's check the grid. Wait, actually, when we reflect \(PQRS\) to get \(WXYZ\), the vertex \(P\) corresponds to \(W\), \(Q\) corresponds to \(X\), \(R\) corresponds to \(Y\), \(S\) corresponds to \(Z\). So side \(QR\) (between \(Q\) and \(R\)) should correspond to side \(XY\) (between \(X\) and \(Y\))? Wait, no, \(Q\) corresponds to \(X\), \(R\) corresponds to \(Y\), so \(QR\) (from \(Q\) to \(R\)) corresponds to \(XY\) (from \(X\) to \(Y\))? Wait, the question is "Which side of figure \(WXYZ\) corresponds with \(QR\)?", and the option given is \(\overline{XY}\), so that's the corresponding side.

Step2: For the angle correspondence

We need to find which angle of \(WXYZ\) corresponds with \(\angle P\). Since \(P\) corresponds to \(W\) (from the reflection, as \(PQRS\) reflected to \(WXYZ\), so vertex \(P\) maps to \(W\)), so \(\angle P\) (at vertex \(P\)) should correspond to \(\angle W\) (at vertex \(W\)) in \(WXYZ\).

Answer:

• Side corresponding to \(QR\): \(\overline{XY}\)
• Angle corresponding to \(\angle P\): \(\angle W\)