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A(1, 2) and C(5, 6) are opposite vertices of square ABCD. Find the other two vertices B and D.

Class 10Classifying Shapes by CoordinatesGeometry — Coordinates
  • A(2, 5) and (4, 3)
  • B(3, 8) and (3, 0)
  • C(1, 6) and (5, 2)
  • D(1, 2) and (5, 6)

Step-by-Step Solution

Centre = (3, 4). The other diagonal is perpendicular to AC with the same half-length : from go (−2, 2) and (2, −2), giving (1, 6) and (5, 2). Check: all sides 4 and diagonals both . (3, 8) and (3, 0) give a rhombus, not a square.
Answer: C) (1, 6) and (5, 2)

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