Slope of Parallel and Perpendicular Lines Worksheet for 9th - 11th ... - Free Printable
Educational worksheet: Slope of Parallel and Perpendicular Lines Worksheet for 9th - 11th .... Download and print for classroom or home learning activities.
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Step-by-step solution for: Slope of Parallel and Perpendicular Lines Worksheet for 9th - 11th ...
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Show Answer Key & Explanations
Step-by-step solution for: Slope of Parallel and Perpendicular Lines Worksheet for 9th - 11th ...
To solve this problem, we need to understand two key rules about slopes of lines:
1. Parallel lines have the same slope.
→ So if a line has slope *m*, any line parallel to it also has slope *m*.
2. Perpendicular lines have slopes that are negative reciprocals of each other.
→ That means: if one line has slope *m*, a perpendicular line has slope *-1/m*.
→ Special case: If a line is horizontal (slope = 0), a perpendicular line is vertical (undefined slope). But in this table, all given slopes are numbers — so we’ll assume no zero or undefined cases unless shown.
Let’s go row by row and fill in the missing data.
---
Row 1: Slope of a line = 8
- Parallel to it? → Same slope → 8
- Perpendicular to it? → Negative reciprocal → -1/8
✔ Check: 8 × (-1/8) = -1 → correct for perpendicular.
---
Row 2: Slope of a line = -5
- Parallel → -5
- Perpendicular → negative reciprocal of -5 → -1/(-5) = 1/5
✔ Check: -5 × (1/5) = -1 → correct.
---
Row 3: Slope of a line = 3
- Parallel → 3
- Perpendicular → -1/3
✔ Check: 3 × (-1/3) = -1 → correct.
---
Row 4: Slope of a line = 1/3
- Parallel → 1/3
- Perpendicular → negative reciprocal → -1/(1/3) = -3
✔ Check: (1/3) × (-3) = -1 → correct.
---
Row 5: Slope of a line = 9
- Parallel → 9
- Perpendicular → -1/9
✔ Check: 9 × (-1/9) = -1 → correct.
---
Row 6: Slope of a line = 4/7
- Parallel → 4/7
- Perpendicular → negative reciprocal → -1/(4/7) = -7/4
✔ Check: (4/7) × (-7/4) = -1 → correct.
---
Row 7: Slope of a line = 6
- Parallel → 6
- Perpendicular → -1/6
✔ Check: 6 × (-1/6) = -1 → correct.
---
Row 8: Slope of a line = -2/3
- Parallel → -2/3
- Perpendicular → negative reciprocal → -1/(-2/3) = 3/2
✔ Check: (-2/3) × (3/2) = -1 → correct.
---
Row 9: Slope of a line = -1
- Parallel → -1
- Perpendicular → negative reciprocal → -1/(-1) = 1
✔ Check: (-1) × 1 = -1 → correct.
---
Row 10: Slope of a line = 1/2
- Parallel → 1/2
- Perpendicular → -1/(1/2) = -2
✔ Check: (1/2) × (-2) = -1 → correct.
---
All calculations checked out.
Final Answer:
| Slope of a line | Slope of any line parallel to it | Slope of any line perpendicular to it |
|------------------|-----------------------------------|----------------------------------------|
| 8 | 8 | -1/8 |
| -5 | -5 | 1/5 |
| 3 | 3 | -1/3 |
| 1/3 | 1/3 | -3 |
| 9 | 9 | -1/9 |
| 4/7 | 4/7 | -7/4 |
| 6 | 6 | -1/6 |
| -2/3 | -2/3 | 3/2 |
| -1 | -1 | 1 |
| 1/2 | 1/2 | -2 |
1. Parallel lines have the same slope.
→ So if a line has slope *m*, any line parallel to it also has slope *m*.
2. Perpendicular lines have slopes that are negative reciprocals of each other.
→ That means: if one line has slope *m*, a perpendicular line has slope *-1/m*.
→ Special case: If a line is horizontal (slope = 0), a perpendicular line is vertical (undefined slope). But in this table, all given slopes are numbers — so we’ll assume no zero or undefined cases unless shown.
Let’s go row by row and fill in the missing data.
---
Row 1: Slope of a line = 8
- Parallel to it? → Same slope → 8
- Perpendicular to it? → Negative reciprocal → -1/8
✔ Check: 8 × (-1/8) = -1 → correct for perpendicular.
---
Row 2: Slope of a line = -5
- Parallel → -5
- Perpendicular → negative reciprocal of -5 → -1/(-5) = 1/5
✔ Check: -5 × (1/5) = -1 → correct.
---
Row 3: Slope of a line = 3
- Parallel → 3
- Perpendicular → -1/3
✔ Check: 3 × (-1/3) = -1 → correct.
---
Row 4: Slope of a line = 1/3
- Parallel → 1/3
- Perpendicular → negative reciprocal → -1/(1/3) = -3
✔ Check: (1/3) × (-3) = -1 → correct.
---
Row 5: Slope of a line = 9
- Parallel → 9
- Perpendicular → -1/9
✔ Check: 9 × (-1/9) = -1 → correct.
---
Row 6: Slope of a line = 4/7
- Parallel → 4/7
- Perpendicular → negative reciprocal → -1/(4/7) = -7/4
✔ Check: (4/7) × (-7/4) = -1 → correct.
---
Row 7: Slope of a line = 6
- Parallel → 6
- Perpendicular → -1/6
✔ Check: 6 × (-1/6) = -1 → correct.
---
Row 8: Slope of a line = -2/3
- Parallel → -2/3
- Perpendicular → negative reciprocal → -1/(-2/3) = 3/2
✔ Check: (-2/3) × (3/2) = -1 → correct.
---
Row 9: Slope of a line = -1
- Parallel → -1
- Perpendicular → negative reciprocal → -1/(-1) = 1
✔ Check: (-1) × 1 = -1 → correct.
---
Row 10: Slope of a line = 1/2
- Parallel → 1/2
- Perpendicular → -1/(1/2) = -2
✔ Check: (1/2) × (-2) = -1 → correct.
---
All calculations checked out.
Final Answer:
| Slope of a line | Slope of any line parallel to it | Slope of any line perpendicular to it |
|------------------|-----------------------------------|----------------------------------------|
| 8 | 8 | -1/8 |
| -5 | -5 | 1/5 |
| 3 | 3 | -1/3 |
| 1/3 | 1/3 | -3 |
| 9 | 9 | -1/9 |
| 4/7 | 4/7 | -7/4 |
| 6 | 6 | -1/6 |
| -2/3 | -2/3 | 3/2 |
| -1 | -1 | 1 |
| 1/2 | 1/2 | -2 |
Parent Tip: Review the logic above to help your child master the concept of parallel and perpendicular lines worksheet with answers.
