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The slopes of two perpendicular lines satisfy which relation?
ASlopes are equal (m₁ = m₂)
BSlopes' product is −1 (m₁ m₂ = −1)
CSlopes sum to 1 (m₁ + m₂ = 1)
DSlopes are reciprocals (m₁ = 1/m₂)
Answer & Solution
Correct answer: B. Slopes' product is −1 (m₁ m₂ = −1)
1. Suppose lines of slopes p and q are perpendicular at point (a, b).
2. Pick (a+1, b+p) on the first line and (a+1, b+q) on the second; these and (a, b) form a right triangle.
3. By Pythagoras: (1² + p²) + (1² + q²) = (q − p)².
4. Simplifying gives 2 + 2pq = 0, hence pq = −1.
5. So the slopes of perpendicular lines multiply to −1.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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