Question

Translate triangle ABC by the directed line segment from D to E. You may use digital tools or draw your answer and embed a screenshot of your work.

Answer 1

If you can observe

• AB=BC=AC

ABC is an equilateral triangle

so

∆DEB is also equilateral triangle

• DE=BD=BE=3.5

Answer 2

The translated triangle A'B'C' is congruent to the original triangle ABC, but it is shifted to the right and up by the amount of the translation vector DE.

Identify the vector representing the translation. This vector is equal to the directed line segment DE. In the image, you can see that the coordinates of D are (2, 1) and the coordinates of E are (5.5, 4.5). Therefore, the vector representing the translation is (3.5, 3.5).

Add the translation vector to the coordinates of each vertex of triangle ABC. For example, the coordinates of point A are (3, 3.5). Adding the translation vector to these coordinates gives you the coordinates of the translated point A', which are (6.5, 7).

Plot the translated triangle A'B'C'. The translated triangle will be congruent to the original triangle ABC, but it will be shifted by the amount of the translation vector.

Here is an image of triangle ABC translated by the directed line segment DE: