To determine the transformations that can map Figure 1 onto Figure 2, we first recognize that since these shapes are congruent parallelograms, they have the same shape and size but may differ in orientation or position.
The possible transformations that can successfully map one shape onto another include:
- Translations: This is a type of transformation that slides a shape from one position to another without rotating or flipping it. If Figure 1 and Figure 2 are identical in orientation but different in position, a translation will align the two figures perfectly.
- Rotations: If the two parallelograms are positioned in a way that one is rotated compared to the other, a rotation transformation around a specific point can map Figure 1 onto Figure 2. The angle of rotation and the center point of rotation would need to be identified to ensure they align correctly.
- Reflections: If Figure 2 is a mirror image of Figure 1 across a specific line (for example, the x-axis or y-axis), then a reflection transformation can be applied to map Figure 1 onto Figure 2. This means that all points on Figure 1 would be flipped over the line of reflection to create Figure 2.
- Combinations of Transformations: Often, a combination of these transformations (e.g., a translation followed by a rotation) can also accomplish the mapping from Figure 1 to Figure 2. Understanding the relative positions of the two figures will assist in defining the correct sequence of transformations.
In conclusion, to successfully map Figure 1 onto Figure 2, one or more of these transformations—translations, rotations, and reflections—can be applied, depending on the specific positions and orientations of the two parallelograms on the coordinate grid.