Which statement about a geometric transformation is correct?

Which statement about a geometric transformation is correct?

• A. A transformation is any movement of a shape on the coordinate plane.
• B. A transformation is a rigid motion only
• C. A transformation never changes position
• D. A transformation is any movement on the coordinate plane, including translation, rotation, reflection, and dilation

Answer: (D)

A geometric transformation is a map that takes every point of a figure to a new point in the plane, and it can move, rotate, flip, or scale the figure. Translation moves the whole figure without changing its size or shape; rotation turns it around a fixed point; reflection flips it across a line; dilation scales it about a center, changing size. Because a transformation can move the figure and/or change its size, the most complete statement is that it includes translations, rotations, reflections, and dilations. The other options are too restrictive or incorrect: a transformation isn’t limited to moving shapes (dilation changes size too); rigid motions exclude dilation; and some transformations do change the position of the figure.

A geometric transformation is a map that takes every point of a figure to a new point in the plane, and it can move, rotate, flip, or scale the figure. Translation moves the whole figure without changing its size or shape; rotation turns it around a fixed point; reflection flips it across a line; dilation scales it about a center, changing size. Because a transformation can move the figure and/or change its size, the most complete statement is that it includes translations, rotations, reflections, and dilations. The other options are too restrictive or incorrect: a transformation isn’t limited to moving shapes (dilation changes size too); rigid motions exclude dilation; and some transformations do change the position of the figure.