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AMO 2027 Grades 9-11 SET 1 - Self-study Question 14

AMO · AMO 2027 Grades 9-11 SET 1 - Self-study

Question 14

The points $(0,1)$ and $(1,2)$ are the coordinates of the adjacent corners of a square. Find the sum of the $y$-coordinates of the points diagonally opposite to $(0,1)$ in a square.

Clarification of the source wording: consider both possible squares on this common side, one on each side of the segment, and add the two resulting $y$-coordinates.

Choose one option.
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6