Plot points in all four quadrants, identify points on the axes and origin, and determine horizontal and vertical distances using absolute differences of coordinates. Apply coordinate rules for translations, reflections across the axes, and quarter- or half-turn rotations about the origin, including sequences of transformations in a specified order, to predict image coordinates and analyze preserved lengths, angles, and shape. Identify congruent figures through rigid motions and equal corresponding measurements, and identify similar figures through proportional corresponding side lengths, congruent angles, and a single scale factor, including dilation.