Advanced MathHardDistance between two intersection points
Advanced Math practice question
In the xy-plane, the graphs of y = x² − 2x and y = 3 intersect at two points. What is the distance between these two points?
Answer: 4
x² − 2x = 3 gives (x − 3)(x + 1) = 0, so the points are (3, 3) and (−1, 3). They share a y-coordinate, so the distance is 3 − (−1) = 4.
Common wrong answers
- If you answered 2
- 2 is the SUM of the x-coordinates, or half the distance.
- If you answered 3
- 3 is one x-coordinate (and the y-value of the line).
- If you answered -3
- −3 is the PRODUCT of the x-coordinates; distance is positive.
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