Reflecting on Coordinate Plane Worksheet | Free - CommonCoreSheets - Free Printable

Explanation:
We are given four problems. In each, we must reflect a shape over either the x-axis or y-axis, and then identify which of the listed coordinate points belong to the reflected shape.

Recall:
- Reflecting a point $(x, y)$ over the x-axis gives $(x, -y)$ — flip the sign of the *y*-coordinate.
- Reflecting a point $(x, y)$ over the y-axis gives $(-x, y)$ — flip the sign of the *x*-coordinate.

Let’s go one by one.

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Problem 1:
Original points: A (3,4), B (8,2), C (10,10)
Reflect over the x-axis → change sign of y-coordinates:

- A' = (3, −4)
- B' = (8, −2)
- C' = (10, −10)

Now look at the answer choices — but wait! The question says:
> The shape above has the following coordinates: A. (3,4) B. (8,2) C. (10,10)
> Reflect the shape over the X axis.

But the answer blanks (1a, 1b, 1c) are for the *reflected* coordinates — not the original ones. So we need to write the reflected coordinates in order.

So:
- 1a: (3, −4)
- 1b: (8, −2)
- 1c: (10, −10)

✔ That’s problem 1.

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Problem 2:
Original points: A (4,−5), B (6,3), C (10,6), D (5,−10)
Reflect over the y-axis → change sign of x-coordinates:

- A' = (−4, −5)
- B' = (−6, 3)
- C' = (−10, 6)
- D' = (−5, −10)

So:
- 2a: (−4, −5)
- 2b: (−6, 3)
- 2c: (−10, 6)
- 2d: (−5, −10)

✔ Problem 2 done.

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Problem 3:
Original points: A (−5,1), B (−9,3), C (−8,10)
Reflect over the x-axis → flip y-sign:

- A' = (−5, −1)
- B' = (−9, −3)
- C' = (−8, −10)

So:
- 3a: (−5, −1)
- 3b: (−9, −3)
- 3c: (−8, −10)

✔ Problem 3 done.

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Problem 4:
Original points: A (0,−3), B (−9,0), C (−6,−9), D (1,−10)
Reflect over the x-axis → flip y-sign:

- A' = (0, 3)
- B' = (−9, 0) → y was 0, stays 0
- C' = (−6, 9)
- D' = (1, 10)

So:
- 4a: (0, 3)
- 4b: (−9, 0)
- 4c: (−6, 9)
- 4d: (1, 10)

✔ Problem 4 done.

Now double-check all signs:

1. (3,4) → (3,−4) ✔
(8,2) → (8,−2) ✔
(10,10) → (10,−10) ✔

2. (4,−5) → (−4,−5) ✔
(6,3) → (−6,3) ✔
(10,6) → (−10,6) ✔
(5,−10) → (−5,−10) ✔

3. (−5,1) → (−5,−1) ✔
(−9,3) → (−9,−3) ✔
(−8,10) → (−8,−10) ✔

4. (0,−3) → (0,3) ✔
(−9,0) → (−9,0) ✔
(−6,−9) → (−6,9) ✔
(1,−10) → (1,10) ✔

All correct.

Final Answer:
1a. (3, -4)
1b. (8, -2)
1c. (10, -10)
2a. (-4, -5)
2b. (-6, 3)
2c. (-10, 6)
2d. (-5, -10)
3a. (-5, -1)
3b. (-9, -3)
3c. (-8, -10)
4a. (0, 3)
4b. (-9, 0)
4c. (-6, 9)
4d. (1, 10)