AlgebraMediumEquation of a line perpendicular to a given line through the origin
Algebra practice question
In the xy-plane, line ℓ is perpendicular to the line 2x + 5y = 10 and passes through the origin. Which of the following is an equation of line ℓ?
- A. 5x − 2y = 0Correct
- B. 2x + 5y = 0
- C. 5x + 2y = 0
- D. 2x − 5y = 0
Answer: A. 5x − 2y = 0
The line 2x + 5y = 10 has slope −2/5, so a perpendicular line has slope 5/2. Through the origin: y = (5/2)x, or 5x − 2y = 0.
Why the other answers are wrong
- B. 2x + 5y = 0
- 2x + 5y = 0 is parallel to the given line, not perpendicular.
- C. 5x + 2y = 0
- 5x + 2y = 0 has slope −5/2, the negative of the perpendicular slope.
- D. 2x − 5y = 0
- 2x − 5y = 0 has slope 2/5, the sign-flipped slope, not the negative reciprocal.
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