Maths · Cartesian system of rectangular coordinates in a plane

The centre of a square is at the origin and vertex is . \) Find the ordinates of

The centre of a square is at the origin and vertex is \( A(2,1) . \) Find the \( c 0 \) ordinates of other vertices of the square

  • A. \( B(1,-2), C(-2,-1), D(-1,-2) \)
  • B. \( B(-1,-2), C(-2,-1), D(-1,-2) \)
  • C. \( B(-1,2), C(-2,-1), D(1,-2) \)
  • D. \( (-1,-2), C(-2,-1), D(1,2) \)

Step-by-step solution

The centre of the square is at the origin. The vertex opposite to A(2,1) is C(-2,-1) because the centre is the midpoint of the diagonal. The other two vertices B and D are obtained by rotating the vector from the centre to A by ±90°. Rotating (2,1) anticlockwise gives (-1,2) for B, and clockwise gives (1,-2) for D. Thus the vertices are A(2,1), B(-1,2), C(-2,-1), D(1,-2). Option C matches these coordinates.
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