Which of the following geometric transformations on a 2D asymmetric polygon in Euclidean space preserves BOTH its handedness (chirality) and its boundary perimeter?
Options:
(A) Planar translation along any direction vector
(B) Planar rotation about an arbitrary center point
(C) Planar reflection across an arbitrary straight line
(D) Uniform isotropic scaling with scale factor k = 1.0
Answer Key:
A, B, D
Step-by-Step Solution & Explanation
1. Direct isometries (rigid motions) preserve distance (perimeter) and orientation/handedness (determinant of transformation matrix $= +1$). Planar translations (A), planar rotations (B), and identity scaling $k = 1.0$ (D) are direct isometries.
2. Reflection (C) is an opposite (indirect) isometry (determinant $= -1$); it inverts the handedness (chirality) of asymmetric planar figures.
Therefore, options A, B, and D satisfy both criteria.