AlgebraVery hardDistance between a line's intercepts
Algebra practice question
In the xy-plane, the line 3x − 4y = 12 crosses the x-axis at point P and the y-axis at point Q. What is the distance between P and Q?
Answer: 5
P: set y = 0, 3x = 12, so P = (4, 0). Q: set x = 0, −4y = 12, so Q = (0, −3). Distance: √(4² + 3²) = 5.
Common wrong answers
- If you answered 1
- 1 is 4 − 3; lengths in a right triangle don't subtract.
- If you answered 7
- 7 is 4 + 3, adding the intercepts' distances from the origin instead of using the Pythagorean theorem.
- If you answered 25
- 25 is 4² + 3²; take the square root.
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