Why do you get a quadrilateral when you rotate or reflect a triangle?

Answer 1

When you rotate or reflect a triangle, the original triangle and its transformed image both occupy the same plane, creating a new shape with four vertices. The original three vertices of the triangle combine with the transformed vertex, resulting in a quadrilateral. This new shape is defined by the points of the original triangle and its reflection or rotation, effectively connecting the two shapes. Thus, the transformation introduces an additional vertex, leading to the formation of a quadrilateral.