Let’s solve each problem step by step. We’re reflecting points across the
x-axis or
y-axis. Here’s how it works:
- When you reflect a point over the
x-axis, the
x-coordinate stays the same, and the
y-coordinate flips sign (positive becomes negative, negative becomes positive).
- Example: (3, 4) → (3, -4)
- When you reflect a point over the
y-axis, the
y-coordinate stays the same, and the
x-coordinate flips sign.
- Example: (3, 4) → (-3, 4)
Now let’s do each problem.
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Problem 1: Reflect across the x-axis
Pre-image points:
- A(2, 2)
- B(3, -4)
- C(5, -2)
Reflecting over x-axis → flip y-signs:
- A’(2, -2)
- B’(3, 4) [because -(-4) = +4]
- C’(5, 2) [because -(-2) = +2]
✔ Check: All x-values stay same, y-values flipped. Correct.
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Problem 2: Reflect across the y-axis
Pre-image points:
- A(-2, 1)
- B(-2, 5)
- C(-5, 3)
Reflecting over y-axis → flip x-signs:
- A’(2, 1) [because -(-2) = +2]
- B’(2, 5) [because -(-2) = +2]
- C’(5, 3) [because -(-5) = +5]
✔ Check: All y-values stay same, x-values flipped. Correct.
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Problem 3: Reflect across the y-axis
Pre-image points:
- R(2, 2)
- S(5, 3)
- T(5, 1)
- V(2, 1)
Reflecting over y-axis → flip x-signs:
- R’(-2, 2)
- S’(-5, 3)
- T’(-5, 1)
- V’(-2, 1)
✔ Check: All y-values unchanged, x-values negated. Correct.
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Final Answer:
1)
A'(2, -2), B'(3, 4), C'(5, 2)
2)
A'(2, 1), B'(2, 5), C'(5, 3)
3)
R'(-2, 2), S'(-5, 3), T'(-5, 1), V'(-2, 1)
Parent Tip: Review the logic above to help your child master the concept of coordinate grid worksheet 6th grade.
