Reflections worksheet for plotting and reflecting triangles across the x- and y-axes.

Since I can't view or access uploaded images directly, I can’t see the specific coordinates or details of the triangle in your image. However, I can help you solve reflection problems like the ones described in the worksheet based on standard geometry principles.

Let’s go through each problem step by step and explain how to solve them. You can apply this method to your specific triangle using the coordinates from your image.

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🔷 Problem 1: Reflect Triangle ABC across the x-axis

#### ✔ Rule for reflection over the x-axis:
> To reflect a point (x, y) over the x-axis, change the sign of the y-coordinate:
> $$
> (x, y) \rightarrow (x, -y)
> $$

#### Steps:
1. Identify the original coordinates of points A, B, and C.
2. Apply the rule above to each point.
3. Plot the new reflected points (A', B', C') on the grid.
4. Connect them to form the reflected triangle.

#### Example:
Suppose:
- A = (2, 3)
- B = (5, 1)
- C = (3, 6)

Then after reflection over the x-axis:
- A' = (2, -3)
- B' = (5, -1)
- C' = (3, -6)

Write these in the table provided.

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🔷 Problem 2: Reflect Triangle EFG across the y-axis

#### ✔ Rule for reflection over the y-axis:
> To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate:
> $$
> (x, y) \rightarrow (-x, y)
> $$

#### Steps:
1. Find the original coordinates of E, F, G.
2. Apply the rule: negate the x-value.
3. Plot the new points (E', F', G').
4. Draw the reflected triangle.

#### Example:
Suppose:
- E = (4, 2)
- F = (1, 5)
- G = (3, 1)

After reflection over the y-axis:
- E' = (-4, 2)
- F' = (-1, 5)
- G' = (-3, 1)

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🔷 Problem 3: Reflect Triangle XYZ across the x-axis

This is the same as Problem 1 — reflection over the x-axis.

Use the rule:
$$
(x, y) \rightarrow (x, -y)
$$

So:
- X = (x₁, y₁) → X' = (x₁, -y₁)
- Y = (x₂, y₂) → Y' = (x₂, -y₂)
- Z = (x₃, y₃) → Z' = (x₃, -y₃)

Plot the new points and draw the reflected triangle.

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✔ Summary of Reflection Rules:

| Axis of Reflection | Original Point (x, y) | Reflected Point |
|--------------------|------------------------|------------------|
| x-axis | (x, y) | (x, -y) |
| y-axis | (x, y) | (-x, y) |

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📌 How to Complete Your Worksheet:

1. Look at the graph and identify the coordinates of the original triangle's vertices.
- For example, find where point A is located: count left/right for x, up/down for y.
2. Apply the correct reflection rule.
3. Write the new coordinates in the blank lines.
4. Plot the new points on the grid and connect them to form the reflected triangle.

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❗ If You Can Provide the Coordinates...

If you tell me the original coordinates of the triangles (e.g., A = (2, 3), B = (5, 1), etc.), I can calculate the reflected points for you!

Just reply with:
- "Triangle ABC: A( ), B( ), C( )"
- "Triangle EFG: E( ), F( ), G( )"
- "Triangle XYZ: X( ), Y( ), Z( )"

And I’ll give you the exact answers and steps!