AlgebraHardParameter from perpendicular lines through the origin
Algebra practice question
In the xy-plane, the line through the origin and (3, 4) is perpendicular to the line through the origin and (a, 3), where a is a constant. What is the value of a?
Answer: -4
The first line has slope 4/3, so the second must have slope −3/4: 3/a = −3/4 → a = −4.
Common wrong answers
- If you answered 4
- 4 has the wrong sign; a positive a would give a positive slope.
- If you answered -2.25
- −2.25 comes from 3/a = −4/3, not taking the reciprocal.
- If you answered -3
- −3 comes from setting a = −3 to match the numerator.
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