CC 6th Grade Math Unit BUNDLE: Coordinate Plane (Reflect, Distance ... - Free Printable

Since I can't view or access images directly, I’ll help you solve the problems based on the description of the worksheet. The worksheet involves reflections of geometric figures over the x-axis and y-axis. Let’s go through each problem step by step.

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🔷 Problem 1: Reflect over 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:
$$
(x, y) \rightarrow (x, -y)
$$

Given pre-image points:

| Pre-Image | Image |
|----------|-------|
| A (-2, 3) | A' |
| B (0, -2) | B' |
| C (4, 1) | C' |

Apply the rule:

- $A(-2, 3) \rightarrow A'(-2, -3)$
- $B(0, -2) \rightarrow B'(0, 2)$
- $C(4, 1) \rightarrow C'(4, -1)$

✔ Answer for Problem 1:
- A': $(-2, -3)$
- B': $(0, 2)$
- C': $(4, -1)$

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🔷 Problem 2: Reflect over 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:
$$
(x, y) \rightarrow (-x, y)
$$

Given pre-image points:

| Pre-Image | Image |
|----------|-------|
| A (-2, 1) | A' |
| B (2, 5) | B' |
| C (-5, 3) | C' |

Apply the rule:

- $A(-2, 1) \rightarrow A'(2, 1)$
- $B(2, 5) \rightarrow B'(-2, 5)$
- $C(-5, 3) \rightarrow C'(5, 3)$

✔ Answer for Problem 2:
- A': $(2, 1)$
- B': $(-2, 5)$
- C': $(5, 3)$

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🔷 Problem 3: Reflect over the x-axis again

Same rule as Problem 1: $(x, y) \rightarrow (x, -y)$

Given pre-image points:

| Pre-Image | Image |
|----------|-------|
| A (1, 3) | A' |
| B (5, 3) | B' |
| T (3, 1) | T' |
| O (2, 1) | O' |

Apply the rule:

- $A(1, 3) \rightarrow A'(1, -3)$
- $B(5, 3) \rightarrow B'(5, -3)$
- $T(3, 1) \rightarrow T'(3, -1)$
- $O(2, 1) \rightarrow O'(2, -1)$

✔ Answer for Problem 3:
- A': $(1, -3)$
- B': $(5, -3)$
- T': $(3, -1)$
- O': $(2, -1)$

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✔ Summary of Answers:

#### Problem 1 (Reflect over x-axis):
- A': $(-2, -3)$
- B': $(0, 2)$
- C': $(4, -1)$

#### Problem 2 (Reflect over y-axis):
- A': $(2, 1)$
- B': $(-2, 5)$
- C': $(5, 3)$

#### Problem 3 (Reflect over x-axis):
- A': $(1, -3)$
- B': $(5, -3)$
- T': $(3, -1)$
- O': $(2, -1)$

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📌 How to Graph (if needed):

For each problem:
1. Plot the original (pre-image) points on the coordinate plane.
2. Apply the reflection rule to find new coordinates.
3. Plot the image points.
4. Connect the points to form the reflected figure.

Let me know if you'd like me to guide you through graphing one of them!