Block Symmetry Sheet 5: Complete the patterns using the mirror lines.

Let's solve the Block Symmetry Sheet 5 step by step.

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🔍 Objective:

Use the two mirror lines (one vertical and one horizontal) to complete each pattern by reflecting the shaded blocks across both lines. This means we are creating reflection symmetry in two directions — like a mirror on the left/right and up/down.

Each grid is divided into four quadrants by:
- A vertical mirror line (down the middle)
- A horizontal mirror line (across the middle)

So, if a block is shaded in one quadrant, its mirror image must be shaded in the opposite quadrant(s), based on the mirror lines.

We will go through each of the five grids one at a time.

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✔ Step-by-step Solution

#### 🟦 Grid 1 (Top Left)
Given: Shaded blocks in the top-right quadrant.

We reflect across:
- Vertical mirror → copy to the left side (same row, mirrored column)
- Horizontal mirror → copy to the bottom side (same column, mirrored row)

So:
- Each shaded block in the top-right should have:
- A mirror in the top-left (left reflection)
- A mirror in the bottom-right (down reflection)
- And finally, a mirror in the bottom-left (both reflections)

👉 So, complete the pattern by mirroring all shaded blocks across both axes.

Result: The full shape will be symmetric in all four quadrants.

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#### 🟦 Grid 2 (Top Right)
Given: Shaded blocks in the top-left quadrant.

Reflect across:
- Vertical mirror → copy to top-right
- Horizontal mirror → copy to bottom-left
- Then both → bottom-right

👉 Complete the pattern by adding the reflected blocks.

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#### 🟦 Grid 3 (Middle Left)
Given: Shaded blocks in the top-left quadrant.

Same process:
- Reflect across vertical → top-right
- Reflect across horizontal → bottom-left
- Both → bottom-right

👉 Mirror all shaded blocks across both lines.

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#### 🟦 Grid 4 (Middle Right)
Given: Shaded blocks in the bottom-right quadrant.

Reflect:
- Across vertical → bottom-left
- Across horizontal → top-right
- Both → top-left

👉 Fill in the other three quadrants accordingly.

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#### 🟦 Grid 5 (Bottom Full Row)
Given: Shaded blocks in the bottom-left quadrant.

Reflect:
- Across vertical → bottom-right
- Across horizontal → top-left
- Both → top-right

👉 Mirror all shaded blocks across both lines.

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🧩 General Rule for All:

For any shaded square at position (row, col):
- Its horizontal mirror is at (total_rows - row, col)
- Its vertical mirror is at (row, total_cols - col)
- Its double mirror is at (total_rows - row, total_cols - col)

Assuming each grid is 8x8, with mirror lines at the center (between columns 4 & 5, and rows 4 & 5).

So, if a block is at (r, c), then:
- Mirror over vertical: (r, 8 - c) [if 0-indexed]
- Mirror over horizontal: (8 - r, c)
- Double mirror: (8 - r, 8 - c)

But since it's easier visually, just use symmetry.

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✔ Final Answer: Completed Patterns

Since I can't draw directly here, I'll describe how to fill in each grid:

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#### ✔ Grid 1 (Top Left)
Shaded in top-right quadrant.
→ Mirror across vertical → fill top-left
→ Mirror across horizontal → fill bottom-right
→ Mirror both → fill bottom-left

✔ Result: Full symmetric shape across both axes.

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#### ✔ Grid 2 (Top Right)
Shaded in top-left
→ Mirror to top-right
→ Mirror to bottom-left
→ Mirror to bottom-right

✔ Full symmetric shape.

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#### ✔ Grid 3 (Middle Left)
Shaded in top-left
→ Mirror to top-right
→ Mirror to bottom-left
→ Mirror to bottom-right

✔ Complete.

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#### ✔ Grid 4 (Middle Right)
Shaded in bottom-right
→ Mirror to bottom-left
→ Mirror to top-right
→ Mirror to top-left

✔ Complete.

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#### ✔ Grid 5 (Bottom Full Row)
Shaded in bottom-left
→ Mirror to bottom-right
→ Mirror to top-left
→ Mirror to top-right

✔ Complete.

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🎯 Summary:

To complete each pattern:
1. Identify the shaded blocks.
2. Reflect them across the vertical mirror line (left ↔ right).
3. Reflect them across the horizontal mirror line (top ↔ bottom).
4. The result should be a fully symmetric design in all four quadrants.

This is rotational and reflective symmetry — the pattern looks the same when reflected over both axes.

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✔ Final Tip:

You can check your work by folding the paper along the mirror lines — the shaded parts should match perfectly.

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If you'd like, I can provide a visual representation using ASCII or text-based grid diagrams for each completed pattern. Let me know!