Explanation:
Let’s solve each part step by step. We need to reflect triangles across the
x-axis or
y-axis, which means flipping them over those lines.
Rule for reflections:
- Reflecting a point
(x, y) across the
x-axis → new point is
(x, –y)
(x stays the same, y changes sign)
- Reflecting a point
(x, y) across the
y-axis → new point is
(–x, y)
(y stays the same, x changes sign)
We’ll read the original coordinates from the graphs. Since this is a worksheet with grids, we assume standard grid where each square is 1 unit.
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Problem 1: Reflect triangle ABC across the x-axis
First, find coordinates of A, B, C from the first graph:
- Point A is at
(–4, 3)
- Point B is at
(–2, 1)
- Point C is at
(–1, 4)
Now reflect across x-axis: change sign of y-coordinates.
- A′ = (–4, –3)
- B′ = (–2, –1)
- C′ = (–1, –4)
✔ Check: The reflected triangle should be below the x-axis, same distance as original above — looks correct.
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Problem 2: Reflect triangle EFG across the y-axis
Find coordinates from second graph:
- Point E is at
(–3, 2)
- Point F is at
(–1, –1)
- Point G is at
(–2, –3)
Reflect across y-axis: change sign of x-coordinates.
- E′ = (3, 2)
- F′ = (1, –1)
- G′ = (2, –3)
✔ Check: Original points are left of y-axis; reflected ones should be right — yes.
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Problem 3: Reflect triangle XYZ across the x-axis
From third graph:
- Point X is at
(2, –2)
- Point Y is at
(4, –1)
- Point Z is at
(3, –4)
Reflect across x-axis: flip y-sign.
- X′ = (2, 2)
- Y′ = (4, 1)
- Z′ = (3, 4)
✔ Check: Original triangle is below x-axis; reflection should be above — correct.
Now fill in the blanks accordingly.
Final Answer:
1. A′ (–4, –3), B′ (–2, –1), C′ (–1, –4)
2. E′ (3, 2), F′ (1, –1), G′ (2, –3)
3. X′ (2, 2), Y′ (4, 1), Z′ (3, 4)
Parent Tip: Review the logic above to help your child master the concept of rotation reflection translation worksheet.
