Question

On observing the identical trapezoids ABCD and A'B'C'D', your friend claims that the trapezoid A'B'C'D' is obtained by the translation of the first trapezoid, i.e., ABCD. Is your friend correct?

• A. No, it is a reflection, as trapezoid ABCD is reflected along the x-axis.
• B. Yes, it is a translation, as trapezoid ABCD is moved 4 units right and 2 units down.
  
• C. No, it is a rotation, as trapezoid ABCD is rotated ${180}^{\circ }$ about the origin in the clockwise direction.
  
• D. Yes, it is a translation, as trapezoid ABCD is moved 4 units down and 2 units right.
  

Answer 1

The correct option is C No, it is a rotation, as trapezoid ABCD is rotated ${180}^{\circ }$ about the origin in the clockwise direction.


No, the claim made by the friend is not correct. Although both the trapezoids have the same measurements, they are not translated, as translation involves shifting or sliding of an object and in this case, their orientation has changed.
In the given figure, the trapezoid A'B'C'D' is obtained by rotating the trapezoid ABCD at an angle of ${180}^{\circ }$ about the origin in the clockwise direction. We know that rotation involves turning an object at a particular angle considering a fixed point as the center of rotation.