Question

1. translate triangle abc by the directed line segment from d to e.

Explanation:

Step1: Determine translation vector

The translation vector is the directed - line segment from \(D\) to \(E\).

Step2: Translate each vertex

For vertex \(A\): Move \(A\) the same distance and direction as the vector \(\overrightarrow{DE}\).
For vertex \(B\): Move \(B\) the same distance and direction as the vector \(\overrightarrow{DE}\).
For vertex \(C\): Move \(C\) the same distance and direction as the vector \(\overrightarrow{DE}\).

Step3: Connect the new vertices

Connect the new positions of \(A\), \(B\), and \(C\) to form the translated triangle.

Answer:

The new triangle formed by the translated vertices of \(\triangle ABC\) following the direction and length of \(\overrightarrow{DE}\).