Of course! I'll solve the worksheet for you and explain the concepts behind the answers.
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📘 Key Concepts:
1.
Parallel Lines: Two lines are parallel if they have the
same slope.
- So, the slope of any line parallel to a given line is
identical to the given slope.
2.
Perpendicular Lines: Two lines are perpendicular if their slopes are
negative reciprocals of each other.
- To find the negative reciprocal:
- Flip the fraction (or write the whole number as a fraction over 1).
- Change the sign (positive becomes negative, negative becomes positive).
> Example: If slope = `3/4`, then perpendicular slope = `-4/3`.
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✔ Now, let’s fill in the table:
| # | Slope of a Line | Slope of Any Parallel Line | Slope of Any Perpendicular Line |
|---|------------------|-----------------------------|----------------------------------|
| 1) | `11/12` | `11/12` | `-12/11` |
| 2) | `6` | `6` | `-1/6` |
| 3) | `5` | `5` | `-1/5` |
| 4) | `12` | `12` | `-1/12` |
| 5) | `5/12` | `5/12` | `-12/5` |
| 6) | `3/7` | `3/7` | `-7/3` |
| 7) | `3` | `3` | `-1/3` |
| 8) | `8` | `8` | `-1/8` |
| 9) | `3/10` | `3/10` | `-10/3` |
|10) | `7/8` | `7/8` | `-8/7` |
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🔍 Explanation for a Few Examples:
-
#1: Given slope = 11/12
- Parallel: same slope → `11/12`
- Perpendicular: flip and change sign → `-12/11`
-
#2: Given slope = 6 (which is 6/1)
- Parallel: `6`
- Perpendicular: flip 6/1 → 1/6, then negate → `-1/6`
-
#5: Given slope = 5/12
- Parallel: `5/12`
- Perpendicular: flip → 12/5, negate → `-12/5`
-
#10: Given slope = 7/8
- Parallel: `7/8`
- Perpendicular: flip → 8/7, negate → `-8/7`
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✔ All answers follow the rules:
-
Parallel = Same slope
-
Perpendicular = Negative reciprocal
Let me know if you’d like to practice more or need a visual graph explanation!
Parent Tip: Review the logic above to help your child master the concept of slopes of parallel and perpendicular lines worksheet.
