Question

a transformation is shown in the diagram. which transformation is shown? quadrilateral defg is translated to form quadrilateral defg. quadrilateral defg is rotated to form quadrilateral defg. quadrilateral defg is reflected to form quadrilateral defg. quadrilateral defg is dilated to form quadrilateral defg.

Explanation:

• Translation: A translation slides a figure without rotating or reflecting it. The orientation of the figure (the order of the vertices, like \(D - E - F - G\)) would remain the same. But in the given transformation, the orientation of the vertices (the "flow" from one vertex to another) has changed.
• Rotation: A rotation turns a figure around a point. When a figure is rotated, the relative positions of its vertices change in a circular - motion - like pattern. Here, quadrilateral \(DEFG\) and \(D'E'FG'\) have the same shape and size (no dilation as there is no change in scale), but the position of the vertices (for example, vertex \(D\) has moved to a new position \(D'\) in a non - sliding, non - reflecting way) is consistent with a rotation.
• Reflection: A reflection flips a figure over a line. If it were a reflection, there would be a line of symmetry such that each point of the original figure has a mirror - image point in the transformed figure. The given transformation does not show a mirror - like flip.
• Dilation: A dilation changes the size of a figure. Since the two quadrilaterals \(DEFG\) and \(D'E'FG'\) have the same size (corresponding sides are equal in length as can be inferred from the diagram), dilation is not the transformation.

Answer:

Quadrilateral \(DEFG\) is rotated to form quadrilateral \(D'E'FG'\).