Perpendicular Lines with Negative Reciprocal Slopes
About This Diagram
This diagram shows three examples of perpendicular lines, demonstrating that perpendicular lines have slopes that are negative reciprocals of each other (their product equals -1).
Examples Shown
| Example | Slope 1 | Slope 2 | Product |
|---|---|---|---|
| 1 | m = 2 | m = -½ | 2 × (-½) = -1 ✓ |
| 2 | m = ¾ | m = -⁴⁄₃ | ¾ × (-⁴⁄₃) = -1 ✓ |
| 3 | m = 0 | undefined | Special case (horizontal ⊥ vertical) |
Finding the Perpendicular Slope
To find the slope of a perpendicular line: 1. Flip the fraction (take the reciprocal) 2. Change the sign (positive ↔ negative)
Examples: - If m = 2 → perpendicular m = -½ - If m = -⅔ → perpendicular m = ³⁄₂
Perpendicular Lines Theorem
Two non-vertical lines are perpendicular if and only if: m₁ × m₂ = -1 or m₂ = -1/m₁
Learning Objectives
- Understand the negative reciprocal relationship between perpendicular slopes
- Apply the theorem to identify and create perpendicular lines
- Analyze the special case of horizontal and vertical lines
Bloom's Taxonomy Level
Understanding, Applying, and Analyzing - Slope relationships.
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