Question

Which of the following rules best describes the translation of ABC to ABC?

A) The rule is "No translation."
B) The rule is "Translate 0 units in any direction."
C) The rule is "Translate ABC to XYZ."
D) The rule is "Translate ABC to ACB."

Answer 1

The correct rule for the translation of triangle ABC to triangle A'B'C' with the same notation is 'No translation,' which means the triangle has not changed position and is the same as 'Translate 0 units in any direction.'

Step-by-step explanation:

The question asks which rule describes the translation of triangle ABC to triangle A'B'C', given that the notation for the triangles remains the same. In geometric translations, an object is moved without rotation or reflection to a new position. The key fact here is that when a translation occurs, and the object's notation remains the same (ABC to ABC), it indicates there was no movement. Therefore, the correct answer is:

A) The rule is "No translation."

This is synonymous with saying:

B) The rule is "Translate 0 units in any direction."

Both A and B effectively convey the same meaning that triangle ABC has not changed its position in the plane.