AlgebraVery hardPerpendicular line through a point
Algebra practice question
Which equation represents the line in the xy-plane that passes through (2, 1) and is perpendicular to the line 2x − y = 3?
- A. x + 2y = 4Correct
- B. 2x − y = 3
- C. x − 2y = 0
- D. 2x + y = 5
Answer: A. x + 2y = 4
2x − y = 3 has slope 2, so a perpendicular has slope −1/2. Through (2, 1): y − 1 = −(1/2)(x − 2), i.e. x + 2y = 4. Check: 2 + 2 = 4 ✓.
Why the other answers are wrong
- B. 2x − y = 3
- 2x − y = 3 is the original line (and (2, 1) is on it), not a perpendicular.
- C. x − 2y = 0
- x − 2y = 0 has slope 1/2, the wrong sign for a perpendicular.
- D. 2x + y = 5
- 2x + y = 5 has slope −2, the negative but not the reciprocal.
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