Answer:
Dilate triangle ABC with scale factor 1/3, then reflect over the line segment CD.
=================================================
Explanation:
We're given that BC = 18 and EC = 6. In order to map ABC onto DEC, we need to have the triangles the same size. In other words, the triangles must be congruent and in the same location. One triangle will be on top of the other.
To make triangle ABC congruent to triangle DEC, we need to have BC = EC. Currently BC is 3 times longer than EC. So we need to dilate with a scale factor 1/3
Note how (1/3)*18 = 6. This scale factor will reduce segment BC so it goes from 18 units long to 6 units long. The same applies to the other segments of triangle ABC.
----------------------
After the dilation, triangle ABC is the same size and shape as triangle DEC. However, the two triangles are not in the same location. We would need point B to be at the same location of point E for the triangles to match up perfectly (point A and point C are already in their proper locations).
To move point B to E, we need to apply a reflection over the horizontal line CD. This will not move points A and C. Points on the line of reflection stay where they are.
---------------------
So to summarize, we apply a dilation with scale factor 1/3 to triangle ABC. This gets triangle ABC to the right size. Then we reflect over the line segment CD so that point B moves to point E's location.
