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 is a slide where every point of the figure moves the same distance in the same direction. The orientation of the figure remains the same.
• Rotation: A rotation turns a figure around a fixed point (the center of rotation). The orientation of the figure changes.
• Reflection: A reflection flips a figure over a line (the line of reflection). The orientation of the figure changes (it is a mirror - image).
• Dilation: A dilation resizes a figure. The figure either gets larger (enlargement) or smaller (reduction).

In the given diagram, quadrilateral \(DEFG\) and \(D'E'F'G'\) have the same shape and size (so it is not a dilation). The orientation of the quadrilateral has changed (so it is not a translation). There is no indication of a mirror - like flip (so it is not a reflection). A rotation changes the orientation of a figure while keeping its shape and size.

Answer:

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