https://file.aiquickdraw.com/mathbot/file/1728222105761gwk99i74.jpg

Let's review the image of the test and analyze the answers provided:

### 1. **Problem 1**
   - **Question**: Determine the translation that maps Figure D onto Figure C.
   - **Student Answer**: Translation 1 unit right, 8 units up, and 2 units down (correction in the test shows "down" corrected).
   - **Feedback**: The student was marked incorrect here, possibly due to an incorrect direction or distance of translation.
   
   **Expected Translation**: You would check the grid and adjust the translation to correctly map Figure D to Figure C. Double-check if the movement was over-counted or under-counted.

---

### 2. **Problem 2**
   - **Question**: Determine a series of transformations that would map Figure Q onto Figure R.
   - **Student Answer**: The student mentions translation 5 units left, a reflection over the x-axis, and rotation, but it seems there are corrections, and the answer was marked incorrect.
   
   **Expected Answer**: The series of transformations may have been out of order or incorrectly applied. Analyzing the figures is necessary to determine the proper transformation series.

---

### 3. **Problem 3**
   - **Question**: Figure V is the result of a transformation on Figure B. Which transformation would accomplish this?
   - **Student Answer**: The student selected option **C: Reflection over the x-axis**.
   - **Feedback**: This was marked correct, so the transformation was correctly identified as a reflection over the x-axis.

---

### 4. **Problem 4**
   - **Question**: What is the image point of (-8, -5) after the transformation T: (x, y) → (x + 2, -y)?
   - **Student Answer**: (-10, 3) marked incorrect.
   
   **Expected Answer**: Applying the transformation T to (-8, -5):
   \[
   x' = x + 2 = -8 + 2 = -6
   \]
   \[
   y' = -y = -(-5) = 5
   \]
   So the correct point is (-6, 5), not (-10, 3).

---

### 5. **Problem 5**
   - **Question**: What is the image point of (-6, 5) after a translation right 2 units and down 4 units?
   - **Student Answer**: (-10, 7), marked incorrect.
   
   **Expected Answer**: Translation involves adding to the x-coordinate and subtracting from the y-coordinate:
   \[
   x' = -6 + 2 = -4
   \]
   \[
   y' = 5 - 4 = 1
   \]
   The correct answer should be (-4, 1), not (-10, 7).

---

Would you like further explanation on any of these transformations? 

### 5 Related Questions:
1. How can I double-check translation distances on a grid?
2. What is the effect of combining a reflection and rotation?
3. Can a transformation sequence include both translations and reflections?
4. How do reflections change coordinates on the x-axis and y-axis?
5. How do I apply a translation in general form (x + a, y + b)?

### Tip:
When working with transformations, it's helpful to break them down into steps and verify the outcome at each stage before proceeding.

Determine the translations and transformations that map figures in the provided test problems.

This page provides solutions to a geometry test involving translations, reflections, and rotations. Learn how to determine transformations mapping figures and points, covering key concepts such as coordinate geometry and the effects of transformations on figures. Suitable for students in Grades 8-10.

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