Question

triangle abc was transformed to create triangle def. which statement is true regarding the side in the image that corresponds to ba?
o bc corresponds to ba because they are about the same length.
o ed corresponds to ba because they are in the same position.
o ef corresponds to ba because the transformation is isometric.
o fd corresponds to ba because the length is not preserved

Explanation:

Step1: Understand transformation properties

A translation is an isometric transformation. Isometric transformations preserve the shape and size of the figure. So, corresponding sides of the original triangle \(ABC\) and the translated triangle \(DEF\) have the same length.

Step2: Analyze each option

• For the option "\(\overline{FD}\) corresponds to \(\overline{BA}\) because the length is not preserved": Since translation is isometric, lengths are preserved. So this option is wrong.
• For the option "\(\overline{EF}\) corresponds to \(\overline{BA}\) because the transformation is isometric": In a translation, we need to check the correct correspondence of vertices. If \(\triangle ABC\) is translated to \(\triangle DEF\), \(A\) corresponds to \(D\), \(B\) corresponds to \(E\), and \(C\) corresponds to \(F\). So this option is wrong.
• For the option "\(\overline{ED}\) corresponds to \(\overline{BA}\) because they are in the same position": Translation changes the position of the figure. So this option is wrong.
• For the option "\(\overline{BC}\) corresponds to \(\overline{EF}\) because they are about the same length": Since translation is isometric, \(BC\) and \(EF\) have the same length. Also, in the translation of \(\triangle ABC\) to \(\triangle DEF\) (\(A

ightarrow D\), \(B
ightarrow E\), \(C
ightarrow F\)), \(\overline{BC}\) and \(\overline{EF}\) are corresponding sides.

Answer:

\(\overline{BC}\) corresponds to \(\overline{EF}\) because they are about the same length (the correct statement is that \(\overline{BC}\) and \(\overline{EF}\) are corresponding sides as translation is an isometric transformation, so their lengths are equal).