The question asks to describe a sequence of transformations that will move the shaded triangle (pre-image) onto the unshaded triangle (image) on the graph.

Observations from the graph:

• The triangles are congruent, meaning they have the same size and shape, so transformations such as reflection, rotation, translation, or a combination of these will map the shaded triangle onto the unshaded one.

Solution:

One possible sequence of transformations is as follows:

1. Reflection: First, reflect the shaded triangle over the x-axis. This will flip the triangle from the top part of the graph (above the x-axis) to the bottom part (below the x-axis), making it closer to the position of the unshaded triangle.
2. Translation: Next, translate the triangle 4 units downwards to align it with the unshaded triangle. The exact movement will depend on the specific coordinates, but visually, it looks like a vertical translation is required.

This sequence of transformations should map the shaded triangle to the unshaded one.

Would you like more details or have any other questions about this problem?

Here are five related questions to expand on this concept:

1. What are the main types of transformations in geometry?
2. How can you determine if a transformation is rigid (preserving size and shape)?
3. Can two triangles be mapped onto each other using more than one transformation sequence?
4. How do you find the line of reflection when reflecting a shape over an axis?
5. What is the difference between rotation and reflection in terms of transformation properties?

Tip: When performing transformations, always check if the orientation of the shape is preserved or reversed. This helps in identifying whether reflection or rotation occurred!