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Let E be the ellipse x²/16 + y²/9 = 1. For three distinct points P, Q, Q' on E, let M(P,Q) be the midpoint of segment PQ and M(P,Q') the midpoint of segment PQ'. Find the maximum possible distance between M(P,Q) and M(P,Q') as the points vary on E.

1. 4
2. 3
3. 5
4. 7/2

Correct answer: 4

Solution

The difference of midpoints equals (Q - Q')/2, so the maximum distance is half the longest chord (the major axis, length 8), giving 4.

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