Worksheet on geometric reflections, showing examples and exercises for students to practice reflecting shapes across a mirror line.

It looks like you've uploaded a worksheet titled "Transformations: Reflections", which is designed to teach students how to reflect shapes over lines of symmetry (such as the x-axis, y-axis, or other lines) on a coordinate grid. The worksheet includes examples, step-by-step instructions, and practice problems.

Since I can't view images directly, I’ll analyze the content based on what’s visible in your description and typical structure of such worksheets. Let me walk through the problem-solving approach for reflections and explain how to solve this type of task.

---

🔍 What Is a Reflection?

A reflection is a transformation that flips a shape over a line (called the line of reflection) to create a mirror image. Common lines of reflection include:
- The x-axis
- The y-axis
- The line y = x
- Any vertical or horizontal line

---

✔ Key Rules for Reflections

| Line of Reflection | Rule for Coordinates |
|--------------------|----------------------|
| Over the x-axis | (x, y) → (x, -y) |
| Over the y-axis | (x, y) → (-x, y) |
| Over y = x | (x, y) → (y, x) |
| Over y = -x | (x, y) → (-y, -x) |

---

📌 Step-by-Step Guide to Reflecting a Shape

Let’s say you're given a shape (like a triangle or rectangle) on a coordinate grid and asked to reflect it over a line.

#### Example Problem:
> Reflect triangle ABC with vertices A(2, 3), B(4, 1), C(1, 5) over the x-axis.

#### Solution Steps:

1. Identify the coordinates of each vertex.
- A(2, 3)
- B(4, 1)
- C(1, 5)

2. Apply the reflection rule for the x-axis:
→ (x, y) → (x, -y)

3. Find the new coordinates:
- A'(2, -3)
- B'(4, -1)
- C'(1, -5)

4. Plot the new points and connect them to form the reflected image.

5. Label the image (e.g., A'B'C').

---

🧩 Practice Problems from the Worksheet

From the layout of the worksheet, here are likely tasks:

#### Task 1: Reflect a shape over the x-axis
- You’re given a shape on a grid.
- Use the rule (x, y) → (x, -y).
- Plot the new points and draw the reflected shape.

#### Task 2: Reflect over the y-axis
- Rule: (x, y) → (-x, y)
- Flip left-right.

#### Task 3: Reflect over y = x
- Rule: (x, y) → (y, x)
- Swap x and y coordinates.

#### Task 4: Reflect over a diagonal or non-axis line (e.g., y = 1 or x = 2)
- For vertical/horizontal lines, use distance from the line.
- E.g., if reflecting over x = 2, then:
- Distance from point to line = |x - 2|
- New x-coordinate = 2 ± distance (on the opposite side)

---

🎯 Tips for Solving These Problems

1. Always label original and image points clearly (use primes: A', B').
2. Use graph paper or coordinate grid carefully.
3. Check symmetry: The line of reflection should be equidistant between original and image points.
4. Double-check coordinates after applying rules.

---

✔ Final Answer Format (for a typical problem):

> Original Points: A(2, 3), B(4, 1), C(1, 5)
> Reflected over x-axis:
> A'(2, -3), B'(4, -1), C'(1, -5)
> Plot these points and draw the triangle.

---

💡 Why This Is Important

Reflections are foundational in geometry and help understand symmetry, congruence, and transformations in real-world applications (e.g., design, art, computer graphics).

---

If you'd like, you can describe a specific problem from the worksheet (e.g., “Reflect this rectangle over the line y = 1”), and I can walk you through solving it step by step!

Let me know!