(Originais Teachy 2024) - Question Medium of Mathematics

During an interdisciplinary activity of Mathematics and Arts, the 7th grade students were challenged to create a mosaic using the hydraulic tile technique, common in art deco style constructions. For the mosaic, each student received pieces in the shape of an equilateral triangle with a side length of 6 centimeters. After completing the mosaic, one of the students noticed that by translating a set of three tiles, forming a parallelogram common in various art deco designs, the resulting figure was also a piece of the mosaic. Considering the original position of the first set of three tiles as the reference point, and knowing that the second set of three tiles was translated 2 centimeters to the right and 4 centimeters upwards, determine the new position of the set of tiles after the translation.