To determine the series of transformations that would map Figure $P$ onto Figure $Q$, let's carefully analyze the image.

Step-by-step process:

1. Reflection:

   • Observing the two figures, it appears that Figure $Q$ is a reflection of Figure $P$ over the x-axis. All points in Figure $P$ are mirrored vertically, flipping their y-coordinates.

2. Translation:

   • After reflecting, Figure $P$ still needs to be translated upwards. Specifically, this would be a vertical translation. The points of Figure $P$ are shifted along the y-axis.

Transformation steps:

• Step 1: Reflect Figure $P$ across the x-axis. This changes the coordinates of every point from $(x, y)$ to $(x, -y)$.

• Step 2: Translate the reflected figure vertically by 5 units upwards. This moves the points along the y-axis from $y'$ to $y' + 5$.

With this, Figure $P$ will align with Figure $Q$.

Would you like further details on the specific points being transformed, or do you have any questions?

Related questions:

1. What are the exact coordinates of Figure $P$ and Figure $Q$ before and after the transformations?
2. How would the transformation differ if it involved a rotation instead of reflection and translation?
3. Can you identify the line of symmetry after the reflection in this case?
4. How do the orientation and size of Figure $P$ and Figure $Q$ compare after the transformations?
5. What would happen if we first translated Figure $P$ before reflecting it?

Tip:

When determining transformations, always check for basic operations like reflection, rotation, and translation, and then see how combinations of these might yield the result.