Question

triangle \\( \triangle a b c \\) is translated 9 units to the left and 3 units up to create \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\).

what is the length of segment \\( \overline { a ^ { prime } b ^ { prime } } \\)?

units

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation. Rigid transformations (translations, rotations, reflections) preserve the lengths of segments and measures of angles. That is, if \(\triangle ABC\) is translated to \(\triangle A'B'C'\), then \(AB = A'B'\), \(BC=B'C'\), and \(AC = A'C'\).

Step2: Identify the length of the corresponding segment in the original triangle

In \(\triangle ABC\), the length of segment \(AB\) is given as \(8\) units.

Answer:

\(8\)