Reflections worksheet for plotting and reflecting triangles on a coordinate grid.

Let’s solve each problem step by step.

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Problem 1: Reflect triangle ABC across the x-axis

First, find the original coordinates of points A, B, and C from the graph.

Looking at the grid:

- Point A is at (2, 5)
- Point B is at (4, 3)
- Point C is at (3, 1)

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

So:

- A (2, 5) → A’ (2, -5)
- B (4, 3) → B’ (4, -3)
- C (3, 1) → C’ (3, -1)

✔ Check: Reflecting over x-axis flips up/down — so positive y becomes negative, negative becomes positive. Correct.

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Problem 2: Reflect triangle EFG across the y-axis

Find original coordinates:

From the graph:

- E is at (-4, 3)
- F is at (-2, 1)
- G is at (-3, -2)

Reflecting across the y-axis: y stays the same, x changes sign.

So:

- E (-4, 3) → E’ (4, 3)
- F (-2, 1) → F’ (2, 1)
- G (-3, -2) → G’ (3, -2)

✔ Check: Reflecting over y-axis flips left/right — so negative x becomes positive, positive becomes negative. Correct.

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Problem 3: Reflect triangle XYZ across the x-axis

Find original coordinates:

From the graph:

- X is at (-1, -3)
- Y is at (-2, -1)
- Z is at (-4, -2)

Reflecting across the x-axis: x stays same, y changes sign.

So:

- X (-1, -3) → X’ (-1, 3)
- Y (-2, -1) → Y’ (-2, 1)
- Z (-4, -2) → Z’ (-4, 2)

✔ Check: Negative y becomes positive — correct for reflection over x-axis.

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Final Answer:

1.
A (2, 5) → A’ (2, -5)
B (4, 3) → B’ (4, -3)
C (3, 1) → C’ (3, -1)

2.
E (-4, 3) → E’ (4, 3)
F (-2, 1) → F’ (2, 1)
G (-3, -2) → G’ (3, -2)

3.
X (-1, -3) → X’ (-1, 3)
Y (-2, -1) → Y’ (-2, 1)
Z (-4, -2) → Z’ (-4, 2)