Question

quadrilateral ( a ^ { prime } b ^ { prime } c ^ { prime } d ^ { prime } ) is the image of quadrilateral ( a b c d ) under a rotation about the origin, ( ( 0,0 ) ).
determine the angle of rotation.

Explanation:

Step1: Recall rotation rules

Rotation about the origin. Positive rotation is counter - clockwise, negative is clockwise.

Step2: Analyze coordinate transformation

Let's take a point (say \(B\)). Assume original coordinates of \(B\) (before rotation) and its image \(B'\).
If we consider the general rule of rotation. A \(270^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\).
By checking multiple points (e.g., if \(A(x_1,y_1)\) and \(A'(y_1,-x_1)\) after rotation), we can confirm.

Answer:

\(270^{\circ}\) clockwise (or \(- 90^{\circ}\) if using standard position with positive counter - clockwise)