It looks like you've uploaded a worksheet titled
"Parallel or Perpendicular?" where the task is to determine whether pairs of lines are
parallel,
perpendicular, or
neither, based on their given slopes.
Let me solve this step-by-step and explain the logic behind each answer.
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🔍 Key Concepts:
1.
Parallel Lines:
Two lines are
parallel if they have the
same slope.
2.
Perpendicular Lines:
Two lines are
perpendicular if the product of their slopes is
-1 (i.e., one slope is the
negative reciprocal of the other).
3.
Neither:
If neither of the above conditions is met, the lines are
neither parallel nor perpendicular.
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Now let's go through each row:
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1. Slope 1: 3, Slope 2: 3
- Same slope →
Parallel
✔ Answer: Parallel
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2. Slope 1: 2, Slope 2: -1/2
- Are they equal? No.
- Product: $ 2 \times (-\frac{1}{2}) = -1 $ → Negative reciprocal!
✔ Answer: Perpendicular
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3. Slope 1: 4, Slope 2: 1/4
- Not equal → not parallel.
- Product: $ 4 \times \frac{1}{4} = 1 $ → Not -1 → not perpendicular.
✘ Answer: Neither
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4. Slope 1: 1/3, Slope 2: -3
- Not equal → not parallel.
- Product: $ \frac{1}{3} \times (-3) = -1 $ → Yes! Negative reciprocal.
✔ Answer: Perpendicular
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5. Slope 1: -2, Slope 2: 1/2
- Not equal.
- Product: $ -2 \times \frac{1}{2} = -1 $ → Yes!
✔ Answer: Perpendicular
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6. Slope 1: -3, Slope 2: -3
- Same slope →
Parallel
✔ Answer: Parallel
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7. Slope 1: 1, Slope 2: -1
- Not equal.
- Product: $ 1 \times (-1) = -1 $ → Yes!
✔ Answer: Perpendicular
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8. Slope 1: 3/5, Slope 2: 5/3
- Not equal.
- Product: $ \frac{3}{5} \times \frac{5}{3} = 1 $ → Not -1 → not perpendicular.
✘ Answer: Neither
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9. Slope 1: -1/3, Slope 2: 3
- Not equal.
- Product: $ -\frac{1}{3} \times 3 = -1 $ → Yes!
✔ Answer: Perpendicular
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10. Slope 1: 2, Slope 2: 2
- Same slope →
Parallel
✔ Answer: Parallel
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✔ Final Answers Table:
| Slope of line 1 | Slope of line 2 | Answer |
|------------------|------------------|--------|
| 3 | 3 | Parallel |
| 2 | -1/2 | Perpendicular |
| 4 | 1/4 | Neither |
| 1/3 | -3 | Perpendicular |
| -2 | 1/2 | Perpendicular |
| -3 | -3 | Parallel |
| 1 | -1 | Perpendicular |
| 3/5 | 5/3 | Neither |
| -1/3 | 3 | Perpendicular |
| 2 | 2 | Parallel |
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📌 Summary:
-
Parallel: When slopes are equal → Rows 1, 6, 10
-
Perpendicular: When product of slopes is -1 → Rows 2, 4, 5, 7, 9
-
Neither: When neither condition holds → Rows 3, 8
Let me know if you'd like this in a printable format or need help with a different version!
Parent Tip: Review the logic above to help your child master the concept of parallel perpendicular or neither worksheet.
