Question

1. a quadrilateral abcd is translated to the right by 2 units to obtain another quadrilateral abcd. which statement is correct? a. the length of $overline{ab}$ must be two units less than the length of $overline{ab}$. b. the length of $overline{ab}$ must be equal to the length of $overline{ab}$. c. the length of $overline{ab}$ must be twice the length of $overline{ab}$. d. the length of $overline{ab}$ must be two units more than the length of $overline{ab}$.

Explanation:

Step1: Recall translation property

Translation is a rigid - motion transformation. In a rigid - motion transformation (such as translation), the shape and size of the figure remain the same. This means that the lengths of corresponding line - segments are equal.
When quadrilateral \(ABCD\) is translated to the right by 2 units to get \(A'B'C'D'\), \(\overline{AB}\) and \(\overline{A'B'}\) are corresponding line - segments.

Answer:

B. The length of \(\overline{A'B'}\) must be equal to the length of \(\overline{AB}\)