Perform and describe translations, reflections, and rotations on a coordinate plane, recognizing these as rigid motions that preserve size and shape.
A translation slides every point of a figure the same distance and direction. A reflection flips a figure over a line, like a mirror. A rotation turns a figure around a fixed point by some angle. All three are called rigid motions, because they preserve the size and shape of a figure -- only its position or orientation changes.
Three coordinate recipes are worth remembering: reflecting over the y-axis flips the sign of x; reflecting over the x-axis flips the sign of y; rotating 180 degrees about the origin flips both signs.
Mastery looks like: Given a point (or simple figure) and a transformation instruction, they correctly compute the new coordinates and explain why size and shape are preserved.
Common stumbles: Reflecting over the wrong axis (flipping y instead of x, or vice versa); forgetting that a 180-degree rotation flips BOTH coordinates, not just one.
See it visually
Interactive, spoken-aloud tools that show this idea in motion.