Reflections of Shapes Worksheet for 7th - 10th Grade | Lesson Planet - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific figure or details of your problem. However, based on the text you've provided, it appears to be a geometry worksheet about reflections of shapes across different lines (such as the x-axis, y-axis, and other lines like $ x = 1 $, $ y = -2 $, etc.).

Let me walk you through how to solve such reflection problems step-by-step, and then you can apply this method to each part.

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🔷 General Concept: Reflections in the Coordinate Plane

To reflect a shape across a line:
- Reflect each vertex of the shape individually.
- Use coordinate rules for common reflections.

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✔ Common Reflection Rules:

| Reflection Across | Rule for Point $(x, y)$ |
|-------------------|--------------------------|
| x-axis | $(x, -y)$ |
| y-axis | $(-x, y)$ |
| Line $x = a$ | $(2a - x, y)$ |
| Line $y = b$ | $(x, 2b - y)$ |

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Now let's go through each problem based on the description you gave:

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1) Reflect across the x-axis

Given: A triangle with vertices at points (let’s assume from typical problems):
Suppose the original triangle has vertices:
A(1, 2), B(3, 4), C(2, 1)

Rule: Reflect over x-axis → $(x, y) \to (x, -y)$

So:
- A(1, 2) → A'(1, -2)
- B(3, 4) → B'(3, -4)
- C(2, 1) → C'(2, -1)

Plot these new points and connect them.

> 💡 Tip: The shape stays the same size and orientation but flips vertically.

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2) Reflect across $x = 5$

This is a vertical line. The rule is:
$(x, y) \to (2 \cdot 5 - x, y) = (10 - x, y)$

Example: If a point is at (3, 2), its image is:
- $x' = 10 - 3 = 7$, so (7, 2)

Apply this to all vertices of the shape.

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3) Reflect across $y = 1$

Horizontal line. Rule:
$(x, y) \to (x, 2 \cdot 1 - y) = (x, 2 - y)$

Example: If a point is (2, 3), then:
- $y' = 2 - 3 = -1$, so (2, -1)

Do this for all points.

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4) Reflect across the y-axis

Rule: $(x, y) \to (-x, y)$

Example: (4, 2) → (-4, 2)

Just flip the sign of the x-coordinate.

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5) Reflect across the x-axis

Given: Points P(2, 1), E(3, 4), A(4, 1), F(3, 0)

Apply rule: $(x, y) \to (x, -y)$

- P(2, 1) → P'(2, -1)
- E(3, 4) → E'(3, -4)
- A(4, 1) → A'(4, -1)
- F(3, 0) → F'(3, 0) ← unchanged since y = 0

Plot these points and draw the reflected quadrilateral.

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6) Reflect across $y = -2$

Rule: $(x, y) \to (x, 2(-2) - y) = (x, -4 - y)$

Example: For point (1, 1):
- $y' = -4 - 1 = -5$ → (1, -5)

Apply to all given points.

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✔ How to Solve Each Problem:

1. Identify the coordinates of all vertices of the shape.
2. Apply the correct transformation rule based on the line of reflection.
3. Plot the new points and connect them in the same order.
4. Label the image (e.g., A', B', C').

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📌 Example Walkthrough:

Suppose in problem #1, the triangle has vertices:
- A(1, 2)
- B(3, 4)
- C(2, 1)

Reflect across x-axis:

- A’ = (1, -2)
- B’ = (3, -4)
- C’ = (2, -1)

Plot these and draw triangle A’B’C’.

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If you can describe the coordinates of the original points or provide the image details (like coordinates of the shape), I can give you exact answers for each problem.

Alternatively, if you want, you can list the coordinates of the shapes in each question, and I’ll compute the reflected points for you!