Trent Thomas - Reflection Worksheets.pdf - Name: Date: Practice ... - Free Printable

Let’s solve this step by step.

We are reflecting points over the x-axis and then over the y-axis.

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Part 1: Reflect each point in the x-axis

When you reflect a point over the x-axis, the x-coordinate stays the same, but the y-coordinate changes sign (positive becomes negative, negative becomes positive).

So rule:
(x, y) → (x, -y)

Given points:

- A (3, 8) → (3, -8)
- B (-2, 4) → (-2, -4)
- C (-6, -2) → (-6, 2)
- D (5, -7) → (5, 7)

✔ So reflections over x-axis:
A’ = (3, -8)
B’ = (-2, -4)
C’ = (-6, 2)
D’ = (5, 7)

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Part 2: Reflect each point in the y-axis

When you reflect a point over the y-axis, the y-coordinate stays the same, but the x-coordinate changes sign.

Rule:
(x, y) → (-x, y)

Same original points:

- A (3, 8) → (-3, 8)
- B (-2, 4) → (2, 4)
- C (-6, -2) → (6, -2)
- D (5, -7) → (-5, -7)

✔ So reflections over y-axis:
A'' = (-3, 8)
B'' = (2, 4)
C'' = (6, -2)
D'' = (-5, -7)

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Final Check:

Let’s double-check one example to be sure.

Take point C (-6, -2):

- Over x-axis: flip y → (-6, 2) ✔
- Over y-axis: flip x → (6, -2) ✔

Another: D (5, -7)

- Over x-axis: (5, 7) ✔
- Over y-axis: (-5, -7) ✔

All good!

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Final Answer:

Reflections in the x-axis:
A’ = (3, -8), B’ = (-2, -4), C’ = (-6, 2), D’ = (5, 7)

Reflections in the y-axis:
A'' = (-3, 8), B'' = (2, 4), C'' = (6, -2), D'' = (-5, -7)