Rhombus PQRS is shown on the coordinate plane. Points M and N are midpoints of their respective sides.
Select ALL of the transformations that map the rhombus onto itself
a 90 degrees clockwise rotation around the center of the rhombus
A 180 degrees clockwise rotation around the center of the rhombus
A reflection across PR
A reflection across NM
a reflection across QS
A 180 degrees clockwise rotation around the center of the rhombus
A reflection across PR
The transformations that map the rhombus onto itself are:
- A 180 degrees clockwise rotation around the center of the rhombus
- A reflection across PR
To determine which transformations map the rhombus onto itself, we need to consider the properties of a rhombus.
1. A 90 degrees clockwise rotation around the center of the rhombus: This transformation does not preserve the shape and size of the rhombus. Therefore, it does not map the rhombus onto itself.
2. A 180 degrees clockwise rotation around the center of the rhombus: This transformation does preserve the shape and size of the rhombus. Each vertex of the rhombus will coincide with its original position after the transformation. Therefore, it maps the rhombus onto itself.
3. A reflection across PR: This transformation interchanges the positions of points P and R while keeping the other points fixed. It preserves the shape and size of the rhombus. Therefore, it maps the rhombus onto itself.
4. A reflection across NM: This transformation interchanges the positions of points N and M while keeping the other points fixed. It preserves the shape and size of the rhombus. Therefore, it maps the rhombus onto itself.
5. A reflection across QS: This transformation does not preserve the shape and size of the rhombus. Therefore, it does not map the rhombus onto itself.
So, the transformations that map the rhombus onto itself are:
- A 180 degrees clockwise rotation around the center of the rhombus
- A reflection across PR
- A reflection across NM