Questions and Answers
What are the coordinates of A' after the 90° counter-clockwise rotation?
A': (-1,1)
What are the coordinates of B' after the 90° counter-clockwise rotation?
B': (-1,2)
What are the coordinates of C' after the 90° counter-clockwise rotation?
C': (-3,2)
What are the coordinates of D' after the 90° counter-clockwise rotation?
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What are the coordinates of A'' after the 180° clockwise rotation?
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What are the coordinates of B'' after the 180° clockwise rotation?
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What are the coordinates of C'' after the 180° clockwise rotation?
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What are the coordinates of D'' after the 180° clockwise rotation?
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How are A'B'C'D' and A''B''C''D'' related?
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Study Notes
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.
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Description
Explore the transformations of trapezoid ABCD through various rotations. This quiz involves rotating the trapezoid 90° counter-clockwise and 180° clockwise about the origin. Show your work to determine the new coordinates after each transformation.