https://file.aiquickdraw.com/mathbot/file/1725904838953zyjz7o0o.jpg

To determine the series of transformations that map **Figure P** onto **Figure Q**, we can break it down by analyzing the visual relationship between the two figures. Let's consider a step-by-step process:

### Step 1: **Rotation**
- The figures are both triangles with identical shapes and orientations, but **Figure Q** is rotated by 180° relative to **Figure P**.
- A **180° rotation** around the origin will map **Figure P** onto a position where it resembles **Figure Q**'s current location in the third quadrant.

### Step 2: **Translation**
- After rotating **Figure P** by 180°, it will be positioned similarly to **Figure Q**, but it will still need a translation to move to its final position.
- The vertices of **Figure P** need to be shifted vertically and horizontally. This can be done by translating it down and to the right.

### Full Transformation Sequence:
- **Rotation by 180° about the origin**, followed by a **translation** (right and down) to align **Figure P** onto **Figure Q**.

Let me know if you'd like further clarification on the transformations!

### Related Questions:
1. How does a 180° rotation affect the coordinates of a figure?
2. What is the general form of a translation in the coordinate plane?
3. How can you determine the exact translation needed after a rotation?
4. What other transformations could map Figure P to Figure Q, if any?
5. How would you describe the relationship between the figures' orientations?

### Tip:
A 180° rotation around the origin changes the sign of both the x and y coordinates of each point.

Determine a series of transformations that would map Figure P onto Figure Q.

Learn how to use a combination of 180° rotation and translation to map Figure P onto Figure Q on a coordinate plane. This problem involves geometric transformations, including rotation and translation, suitable for students in Grades 7-10.

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