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.

Step2: Relate \(AB\) and \(A'B'\)

Since \(\triangle ABC\) is translated to get \(\triangle A'B'C'\), by the property of translation, \(AB = A'B'\).
From the figure, the length of \(AB\) is \(8\) units.

Answer:

\(8\)