(Originais Teachy 2024) - Question Hard of Mathematics

During an interdisciplinary project in mathematics and arts, the 7th grade students decided to create an installation in the schoolyard that explored translation concepts in the Cartesian plane, using geometric figures printed on acrylic plates. The initial proposal was to compose a design with equilateral triangles that, when translated in a specific direction, formed interesting symmetrical patterns. The group had already designed the first stage of the installation, which consisted of a base formed by seven of these juxtaposed triangles, forming a regular hexagon, as shown in Figure 1. Now, the students need to determine the coordinates of the vertices of a second hexagon, which will be obtained from the first one through a translation that moves each vertex 4 units to the right and 2 units up. Considering that the original hexagon is centered at the origin of the Cartesian plane and that the vertices are arranged clockwise from the point (0, 3√3), which is the upper right vertex of the original hexagon, what will be the new position of the vertex that was initially at (-3, 3√3)?