EXPLAINER · QUICK READ

Transformations: Translations, Rotations, and Reflections

5 min readGrade 6 · Geometry

Slide a shape left or right (translation). Spin it around a point (rotation). Flip it over a line (reflection). These are the three basic ways to move shapes on a plane.

Translation (Slide)

A translation moves every point of a shape the same distance in the same direction. If you translate a triangle 3 units right and 2 units up, every vertex moves right 3 and up 2. The shape doesn't rotate or flip—it stays the same size and orientation.

Rotation (Turn)

A rotation turns a shape around a point (usually the origin or a vertex). Rotations are measured in degrees: 90° (quarter turn), 180° (half turn), 270° (three-quarter turn), 360° (full turn). The shape stays the same size; only its orientation changes.

Reflection (Flip)

A reflection flips a shape over a line (usually the x-axis, y-axis, or y = x). Each point moves to the opposite side of the line, the same distance away. The reflected image is a mirror image of the original.

KEY VOCABULARY

Translation — A slide transformation that moves every point the same distance in the same direction.

Rotation — A turn transformation around a point (center of rotation), measured in degrees.

Reflection — A flip transformation over a line (line of reflection), creating a mirror image.

Coordinate plane — A grid with an x-axis and y-axis, where points are located using ordered pairs (x, y).

Ordered pair — A pair of numbers (x, y) that locate a point on a coordinate plane.