Straight Lines
Easymathematics
Two lines with slopes m₁ and m₂ are perpendicular if
Select the correct option:
Solution
Incorrect! Answer:
m₁m₂ = -1
- Geometric Principle: If two lines making angles θ1 and θ2 with the positive x-axis are perpendicular, then ∣θ1−θ2∣=90∘.
- Tangent Relation: tanθ1=m1 and tanθ2=m2.
- Perpendicularity Condition: For non-vertical lines, the product of their slopes must be −1 (m1m2=−1).
- Meaning: This implies one slope is the negative reciprocal of the other (m2=−1/m1).
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- straight lines
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
m₁m₂ = -1
- Geometric Principle: If two lines making angles θ1 and θ2 with the positive x-axis are perpendicular, then ∣θ1−θ2∣=90∘.
- Tangent Relation: tanθ1=m1 and tanθ2=m2.
- Perpendicularity Condition: For non-vertical lines, the product of their slopes must be −1 (m1m2=−1).
- Meaning: This implies one slope is the negative reciprocal of the other (m2=−1/m1).
This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of straight lines. It appeared in the 2025 exam.
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