5.7 (Reflecting Points in the Coordinate Plane) - Free Printable

Explanation:
We are reflecting points across the x-axis and the y-axis. Let’s remember the rules:

- Reflection over the x-axis:
Keep the *x*-coordinate the same, but flip the sign of the *y*-coordinate.
So, $(x, y) \rightarrow (x, -y)$

- Reflection over the y-axis:
Keep the *y*-coordinate the same, but flip the sign of the *x*-coordinate.
So, $(x, y) \rightarrow (-x, y)$

Now let’s apply this to each point.

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First section: Reflect in the x-axis

Given points:
- A: $(1, 3)$ → reflect over x-axis → $(1, -3)$
- B: $(-2, -2)$ → reflect over x-axis → $(-2, 2)$
- C: $(-4, 5)$ → reflect over x-axis → $(-4, -5)$
- D: $(2, -5)$ → reflect over x-axis → $(2, 5)$

(These match what’s handwritten in the image — good check!)

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Second section: Reflect in the y-axis

Same points:
- A: $(1, 3)$ → reflect over y-axis → $(-1, 3)$
- B: $(-2, -2)$ → reflect over y-axis → $(2, -2)$
- C: $(-4, 5)$ → reflect over y-axis → $(4, 5)$
- D: $(2, -5)$ → reflect over y-axis → $(-2, -5)$

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Third section: Table with three ordered pairs

We need both reflections for each:

1. $(-12, 13)$
- x-axis reflection: $(-12, -13)$
- y-axis reflection: $(12, 13)$

2. $(4, -9)$
- x-axis reflection: $(4, 9)$
- y-axis reflection: $(-4, -9)$

3. $(-10, -8)$
- x-axis reflection: $(-10, 8)$
- y-axis reflection: $(10, -8)$

Let me double-check each:

- $(-12, 13)$ → x-axis: y flips → $-13$ ✔
y-axis: x flips → $12$ ✔
- $(4, -9)$ → x-axis: $-9 \to 9$ ✔; y-axis: $4 \to -4$ ✔
- $(-10, -8)$ → x-axis: $-8 \to 8$ ✔; y-axis: $-10 \to 10$ ✔

All correct.

Final Answer:
For the table:
- $(-12, 13)$ → x-axis: $(-12, -13)$, y-axis: $(12, 13)$
- $(4, -9)$ → x-axis: $(4, 9)$, y-axis: $(-4, -9)$
- $(-10, -8)$ → x-axis: $(-10, 8)$, y-axis: $(10, -8)$