Reflection exercise: complete each shape by reflecting it across the dotted line of symmetry.

Let's solve the reflection problem step by step. The task is to complete each shape by reflecting it across the dotted line, which acts as the axis of symmetry.

We'll go through each diagram (a), (b), (c), and (d) and explain how to reflect the given shape across the dotted line.

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🔍 Key Concept: Reflection Across a Line

To reflect a shape across a vertical axis of symmetry:
- For each point on the original shape, measure its horizontal distance to the dotted line.
- On the opposite side of the line, plot a point at the same distance.
- Connect these reflected points to form the mirror image.

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✔ Step-by-Step Solution

#### (a) Right Triangle
- The triangle is on the left side of the dotted line.
- It has three vertices. Let’s assume grid coordinates (for clarity):
- Bottom-left corner: (1,1)
- Top-left corner: (1,3)
- Bottom-right corner: (3,1)
- The dotted line is at x = 5 (assuming grid starts at x=0).
- Distance from each point to the line:
- From x=1 to x=5 → 4 units left
- So reflected points will be 4 units right of the line → x = 5 + 4 = 9
- Reflected vertices:
- (1,1) → (9,1)
- (1,3) → (9,3)
- (3,1) → (7,1)
- Draw a triangle with vertices at (9,1), (9,3), and (7,1).

✔ Result: A mirror image of the triangle on the right side of the line.

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#### (b) Diamond (Rhombus)
- The diamond is centered around the dotted line, but only half is shown.
- It appears symmetric vertically — the left half is visible.
- The shape touches the dotted line at its center.
- To complete:
- Reflect each vertex across the line.
- Since it's symmetric, the right half will be a mirror of the left.
- The top and bottom points are already on the line? No — actually, the shape extends to the left of the line.
- Suppose the leftmost point is at x=4, and the line is at x=6.
- Then the reflected point will be at x=8 (same distance on the other side).
- So, for each vertex:
- If a point is at (4, y), its reflection is at (8, y)
- If at (5, y), reflection is at (7, y)
- Draw the right half accordingly.

✔ Result: Complete diamond symmetric about the dotted line.

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#### (c) Trapezoid (Tilted)
- The trapezoid is on the left side of the dotted line.
- It has two parallel sides (top and bottom), and slanted sides.
- Identify the four corners:
- Left-bottom: (2,1)
- Left-top: (2,3)
- Right-bottom: (4,1)
- Right-top: (4,3)
- Dotted line is at x=6.
- Distance from each point to x=6:
- Points at x=2 → 4 units left → reflect to x=10
- Points at x=4 → 2 units left → reflect to x=8
- Reflected vertices:
- (2,1) → (10,1)
- (2,3) → (10,3)
- (4,1) → (8,1)
- (4,3) → (8,3)
- Connect them to form the mirrored trapezoid on the right.

✔ Result: A symmetrical trapezoid on the right side.

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#### (d) Arrow
- The arrow is pointing to the right, and is on the right side of the dotted line.
- But the left side is missing — so we need to reflect it to the left of the line.
- The arrow has:
- A rectangular shaft and a triangular head.
- Find key points:
- The tip of the arrow is at (7,2)
- The back end of the shaft is at (4,2)
- The top and bottom edges of the shaft and head.
- Dotted line is at x=4.
- So:
- Point at x=7 → 3 units right of line → reflect to x=1
- Point at x=4 → on the line → stays at x=4
- So:
- Tip (7,2) → (1,2)
- Back (4,2) → (4,2)
- Other points: e.g., (6,1) → (2,1), (6,3) → (2,3), etc.
- Draw the reflected arrow pointing to the left.

✔ Result: A mirror image of the arrow on the left side, pointing left.

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🧩 Final Answer Summary:

For each part, you should draw the mirror image of the shape across the dotted line:

| Part | Original Side | Reflection Side |
|------|----------------|------------------|
| (a) | Left triangle | Right triangle |
| (b) | Left half of diamond | Right half completed |
| (c) | Left trapezoid | Right trapezoid |
| (d) | Right-pointing arrow | Left-pointing arrow |

> 💡 Tip: Use graph paper or grid lines to count squares and ensure accurate reflections.

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✔ How to Draw:

1. Pick each corner point of the shape.
2. Count how many squares it is from the dotted line.
3. Go the same number of squares on the other side.
4. Mark the reflected point.
5. Connect the reflected points in order.

This completes all shapes using reflection symmetry.

Let me know if you'd like a visual sketch description or coordinates!