Question

which is true about rigid transformations and circles?
a a reflection of a circle does not conserve the circle’s radius.
b a circle is only carried onto itself after each one degree rotation.
c a translation of a circle does not conserve the circle’s circumference.
d a circles shape is preserved regardless of any rigid transformation.

Explanation:

• Option A: Rigid transformations (like reflection) conserve length, so a circle's radius is conserved. So A is false.
• Option B: A circle can be rotated by any angle (not just 1°) and map onto itself because of its rotational symmetry. So B is false.
• Option C: Translation is a rigid transformation, so a circle's circumference (related to radius) is conserved. So C is false.
• Option D: Rigid transformations (reflection, rotation, translation) preserve shape and size. A circle's shape (being a circle) is preserved under any rigid transformation. So D is true.

Answer:

D. A circle's shape is preserved regardless of any rigid transformation.