Problem 24 · 2003 AMC 8
Stretch
Geometry & Measurement
spatial-reasoning
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Answer: B — the constant-then-dip graph.
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Hint 1 of 2
Don't read the graph as the ship's position — it's the ship's distance from X. Track only how that one distance rises and falls on each leg.
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Hint 2 of 2
On a circle centered at X every point is the same distance away (a flat line); on a straight line the distance to an off-line point falls to a minimum, then rises.
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Approach: read the graph as distance-from-X, leg by leg
- Leg 1, A to B along the semicircle centered at X: every point of a circle is exactly one radius from the center, so the distance to X never changes — a flat horizontal segment.
- Leg 2, B to C in a straight line: the ship's distance to the off-line point X drops as it approaches the closest point on the line (the foot of the perpendicular from X), reaches a minimum there, then climbs again — a smooth dip down and back up.
- A flat stretch followed by a dip matches graph B.
- Worth keeping: "distance vs. time" graphs reward checking each segment's shape separately — constant on an arc around the center, and a single minimum (never a corner) as you pass nearest a fixed point on a straight path.
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