Practice Reflecting Points In The Coordinate Plane - Fill and Sign ... - Free Printable

Let's solve the problem step by step based on the worksheet titled "Practice: Reflecting Points in the Coordinate Plane."

We are asked to:

1. Graph each point and reflect it in the x-axis.
2. Graph each point and reflect it in the y-axis.
3. Reflect points in both the x-axis and y-axis, and record their coordinates.

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🔷 Part 1: Reflect in the x-axis

When a point is reflected over the x-axis, the x-coordinate stays the same, and the y-coordinate changes sign.

So, reflection rule for x-axis:
> (x, y) → (x, -y)

Let’s apply this:

#### A) (1, 3)
- Reflection in x-axis: (1, -3)

#### B) (3, -2)
- Reflection in x-axis: (3, 2)

#### C) (-4, 8)
- Reflection in x-axis: (-4, -8)

#### D) (2, -5)
- Reflection in x-axis: (2, 5)

✔ Answers:
- A) (1, 3) → (1, -3)
- B) (3, -2) → (3, 2)
- C) (-4, 8) → (-4, -8)
- D) (2, -5) → (2, 5)

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🔷 Part 2: Reflect in the y-axis

When a point is reflected over the y-axis, the y-coordinate stays the same, and the x-coordinate changes sign.

Reflection rule for y-axis:
> (x, y) → (-x, y)

Now apply:

#### A) (1, 3)
- Reflection in y-axis: (-1, 3)

#### B) (3, -2)
- Reflection in y-axis: (-3, -2)

#### C) (-4, 8)
- Reflection in y-axis: (4, 8)

#### D) (2, -5)
- Reflection in y-axis: (-2, -5)

✔ Answers:
- A) (1, 3) → (-1, 3)
- B) (3, -2) → (-3, -2)
- C) (-4, 8) → (4, 8)
- D) (2, -5) → (-2, -5)

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🔷 Part 3: Reflect in both x-axis and y-axis

We’re given three ordered pairs. For each, we need to find:
- Reflection in the x-axis
- Reflection in the y-axis

We'll use the rules above.

| Ordered Pair | Reflection in x-axis | Reflection in y-axis |
|--------------|----------------------|----------------------|
| (2, 1) | (2, -1) | (-2, 1) |
| (4, 9) | (4, -9) | (-4, 9) |
| (-10, -8) | (-10, 8) | (10, -8) |

✔ Explanation:

- (2, 1):
- x-axis: (2, -1)
- y-axis: (-2, 1)

- (4, 9):
- x-axis: (4, -9)
- y-axis: (-4, 9)

- (-10, -8):
- x-axis: (-10, 8)
- y-axis: (10, -8)

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✔ Final Answer Table

| Ordered Pair | Reflection in x-axis | Reflection in y-axis |
|--------------|----------------------|----------------------|
| (2, 1) | (2, -1) | (-2, 1) |
| (4, 9) | (4, -9) | (-4, 9) |
| (-10, -8) | (-10, 8) | (10, -8) |

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📌 Summary of Rules

- Reflect over x-axis: Change the sign of y: (x, y) → (x, -y)
- Reflect over y-axis: Change the sign of x: (x, y) → (-x, y)

These reflections are symmetrical across the respective axes.

You can now fill out the worksheet with these answers. Let me know if you’d like a visual explanation or graph!