AlgebraVery hardPoint on a line equidistant from both axes
Algebra practice question
In the xy-plane, point P lies on the line 3x − 4y = 12, is in quadrant IV, and is the same distance from the x-axis as from the y-axis. What is the sum of the coordinates of P?
Answer: 0
In quadrant IV with equal distances, P = (t, −t) for some t > 0. Then 3t + 4t = 12 → t = 12/7, so P = (12/7, −12/7) and the coordinates sum to 0.
Common wrong answers
- If you answered 4
- 4 is the x-intercept of the line, which is on the axis, not equidistant from both.
- If you answered 12/7
- 12/7 is the x-coordinate alone.
- If you answered 24/7
- 24/7 is the difference of the coordinates.
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