3
algebra

Two lines have slopes m1=am_1 = a and m2=1/am_2 = 1/a. Are they perpendicular?

A

No, unless a=1a = -1 or a=1a = 1 (with sign change)

B

Yes, always

C

No, never

D

Only if a=0a = 0

Correct Answer: A

Choice A is the correct answer. Check product rule.

  1. Product: a×(1/a)=1a \times (1/a) = 1.
  2. Condition: Perpendicular lines must have a product of 1-1.
  3. Conclusion: They are reciprocals, but not negative reciprocals. So generally No.

💡 Strategic Tip: Don't forget the negative sign! mm and 1/m-1/m are perpendicular.

Choice B is incorrect because product is 1. Choice C is incorrect because they could be if aa involves complex numbers (out of scope) or specific sign errors in setup. Choice D is incorrect because undefined.