Advanced MathHardSum of coordinates of an intersection point
Advanced Math practice question
In the xy-plane, the circle x² + y² = 50 and the line y = x intersect at two points. What is the sum of the x-coordinate and the y-coordinate of the intersection point that lies in the first quadrant?
Answer: 10
Substituting y = x: 2x² = 50, x² = 25, x = ±5. In the first quadrant the point is (5, 5), and 5 + 5 = 10.
Common wrong answers
- If you answered 0
- 0 would be the sum for (5, −5), but that point is not on the line y = x.
- If you answered 5
- 5 is one coordinate alone.
- If you answered 25
- 25 is x², not a coordinate.
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