Question

tony tried to define a translation.

• point a maps to point a.
• every point p maps to point p such that \\(\overrightarrow{pp}\\) is parallel to \\(\overrightarrow{aa}\\) and points in the same direction as \\(\overrightarrow{aa}\\).

what mistake did tony make in his definition of a translation?
choose 1 answer:
a tony needed to mention that the center of translation maps to itself.
b \\(\overline{pp}\\) must have the same length as \\(\overline{aa}\\).
c \\(\overrightarrow{pp}\\) must be perpendicular to \\(\overrightarrow{aa}\\).
d tony did not make a mistake.

Explanation:

A translation in geometry is a transformation where every point of a figure is moved the same distance in the same direction. Tony's definition says \(\overrightarrow{PP'}\) is parallel and same - direction as \(\overrightarrow{AA'}\), but he missed that the length of \(\overrightarrow{PP'}\) must equal the length of \(\overrightarrow{AA'}\). Option A is wrong because translation has no center (rotations have centers), option C is wrong as \(\overrightarrow{PP'}\) should be parallel, not perpendicular, and option D is wrong as there is a mistake.

Answer:

B. \(\overline{PP'}\) must have the same length as \(\overline{AA'}\).