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Geometry Trapezoid Transformations

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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?

D': (-3,0) Signup and view all the answers

What are the coordinates of A'' after the 180° clockwise rotation?

A'': (-1,-1) Signup and view all the answers

What are the coordinates of B'' after the 180° clockwise rotation?

B'': (-2,-1) Signup and view all the answers

What are the coordinates of C'' after the 180° clockwise rotation?

C'': (-2,-3) Signup and view all the answers

What are the coordinates of D'' after the 180° clockwise rotation?

D'': (0,-3) Signup and view all the answers

How are A'B'C'D' and A''B''C''D'' related?

A'B'C'D' and A''B''C''D'' are reflections of each other over the y-axis. Signup and view all the answers

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.