How do transformations affect the area of geometric shapes?

The correct answer highlights an important principle regarding transformations in geometry. Non-rigid transformations, such as dilation (scaling), do affect the area of geometric shapes. When a shape undergoes a non-rigid transformation, its dimensions might be altered, resulting in an increase or decrease in area. For instance, if a triangle is dilated by a scale factor greater than one, its area becomes larger because the lengths of its sides are multiplied, which in turn affects the area calculation based on those new dimensions.

In contrast, rigid transformations, which include translations, rotations, and reflections, do not change the size or shape of the geometric figure, which means the area remains constant. These transformations simply reposition the shape in space without altering its fundamental properties.

Choosing this answer reflects an understanding of how different types of transformations impact geometric figures, particularly in regards to area.