Reflections worksheet for practicing geometric transformations on coordinate planes.

Since I can't view or access images directly, I’ll help you solve the reflection problems based on the description of the worksheet. Let’s go through each problem step by step.

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Reflections Worksheet – Step-by-Step Solution

We are asked to reflect triangles across either the x-axis or y-axis, record the new coordinates, and draw the reflected triangle.

Let’s assume the original points for each triangle are visible in the image (since you mentioned an uploaded image). Since I don’t have the exact coordinates from the image, I will assume typical values based on common problems like this, and then show how to solve it. If you provide the actual coordinates, I can adjust accordingly.

But let’s suppose from the graph:

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Problem 1: Reflect Triangle ABC across the x-axis

Assume the original triangle ABC has these points (based on typical graphs):

- A = (-2, 4)
- B = (0, 1)
- C = (-3, -1)

#### 🔹 Rule for reflection over the x-axis:
> To reflect a point over the x-axis, keep the x-coordinate the same, and change the sign of the y-coordinate.
>
> So:
> (x, y) → (x, -y)

Apply this rule:

- A(-2, 4) → A'(-2, -4)
- B(0, 1) → B'(0, -1)
- C(-3, -1) → C'(-3, 1)

✔ Recorded new points:
- A’ = (-2, -4)
- B’ = (0, -1)
- C’ = (-3, 1)

Then plot these points and draw triangle A'B'C'.

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Problem 2: Reflect Triangle EFG across the y-axis

Assume the original triangle EFG has:

- E = (4, 3)
- F = (6, 1)
- G = (2, -2)

#### 🔹 Rule for reflection over the y-axis:
> To reflect a point over the y-axis, keep the y-coordinate the same, and change the sign of the x-coordinate.
>
> So:
> (x, y) → (-x, y)

Apply this rule:

- E(4, 3) → E'(-4, 3)
- F(6, 1) → F'(-6, 1)
- G(2, -2) → G'(-2, -2)

✔ Recorded new points:
- E’ = (-4, 3)
- F’ = (-6, 1)
- G’ = (-2, -2)

Plot these and draw triangle E'F'G'.

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Problem 3: Reflect Triangle XYZ across the x-axis

Assume the original triangle XYZ has:

- X = (1, 2)
- Y = (4, 5)
- Z = (3, -1)

#### 🔹 Again, reflection over the x-axis: (x, y) → (x, -y)

So:

- X(1, 2) → X'(1, -2)
- Y(4, 5) → Y'(4, -5)
- Z(3, -1) → Z'(3, 1)

✔ Recorded new points:
- X’ = (1, -2)
- Y’ = (4, -5)
- Z’ = (3, 1)

Plot and draw triangle X'Y'Z'.

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✔ Summary of Rules:

| Reflection | Rule |
|----------|------|
| Over x-axis | (x, y) → (x, -y) |
| Over y-axis | (x, y) → (-x, y) |

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📌 Final Answer Format (as per worksheet):

#### 1. Triangle ABC reflected over x-axis:
- A(_____) → A'(_____)
- B(_____) → B'(_____)
- C(_____) → C'(_____)

Example (with assumed values):
- A(-2, 4) → A'(-2, -4)
- B(0, 1) → B'(0, -1)
- C(-3, -1) → C'(-3, 1)

#### 2. Triangle EFG reflected over y-axis:
- E(_____) → E'(_____)
- F(_____) → F'(_____)
- G(_____) → G'(_____)

Example:
- E(4, 3) → E'(-4, 3)
- F(6, 1) → F'(-6, 1)
- G(2, -2) → G'(-2, -2)

#### 3. Triangle XYZ reflected over x-axis:
- X(_____) → X'(_____)
- Y(_____) → Y'(_____)
- Z(_____) → Z'(_____)

Example:
- X(1, 2) → X'(1, -2)
- Y(4, 5) → Y'(4, -5)
- Z(3, -1) → Z'(3, 1)

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🔍 How to Use This:

1. Look at your actual graph and read the coordinates of the original triangle.
2. Apply the correct reflection rule.
3. Plot the new points and draw the reflected triangle.

If you can provide the actual coordinates from the image (e.g., "A is at (-2, 4)", etc.), I can give you the exact answers for your specific case.

Let me know!