Geometry Trapezoid Transformations

Trapezoid Rotation and Coordinates

• Trapezoid ABCD has vertices at A(1,1), B(2,1), C(2,3), and D(0,3) on the coordinate plane.
• Rotating the trapezoid 90° counter-clockwise about the origin results in new coordinates:
  • A' at (-1,1)
  • B' at (-1,2)
  • C' at (-3,2)
  • D' at (-3,0)

Further Rotations

• A subsequent rotation of the trapezoid 180° clockwise also influences the coordinates:
  • A" becomes (-1,-1)
  • B" becomes (-2,-1)
  • C" becomes (-2,-3)
  • D" becomes (0,-3)

Relationship Between Figures

• The figures A'B'C'D' and A"B"C"D" are reflections of each other across the y-axis.
• Understanding these transformations highlights geometric properties and symmetries in coordinate planes.