Question

how was pre - image wxyz transformed to create image wxyz?
90° clockwise rotation around point b
180° clockwise rotation around point b
reflection over line a
translation up

Explanation:

Step1: Analyze translation

Translation up would just move the figure vertically. But the orientation of the figure has changed (the shape is rotated in a sense), so translation up is not the transformation.

Step2: Analyze reflection

Reflection over line \(a\) would flip the figure over the line. But looking at the pre - image \(WXYZ\) and image \(W'X'Y'Z'\), it is not a simple flip over a vertical line (since the relative positions of the vertices with respect to a vertical line are not consistent with a reflection).

Step3: Analyze \(90^{\circ}\) and \(180^{\circ}\) rotations

• For a \(90^{\circ}\) clockwise rotation formula about a point \((x,y)\) (if rotating about a point \(B\)): If we assume a general point \((x,y)\) and a center of rotation \((h,k)\), the formula is \((x',y')=(h+(y - k),k-(x - h))\).
• For a \(180^{\circ}\) clockwise rotation formula about a point \((h,k)\): \((x',y')=(2h - x,2k - y)\).

By visual inspection of the pre - image \(WXYZ\) and image \(W'X'Y'Z'\), a \(180^{\circ}\) clockwise rotation around point \(B\) would change the orientation of the figure in a way that is not consistent with what we see.

• For a \(90^{\circ}\) clockwise rotation around point \(B\), if we consider the movement of the vertices of the pre - image \(WXYZ\) to the image \(W'X'Y'Z'\), we can observe that the transformation rule of a \(90^{\circ}\) clockwise rotation (using the concept of rotation of geometric figures in a coordinate - like plane) matches the given pre - image and image.

Answer:

\(90^{\circ}\) clockwise rotation around point \(B\)