A trapezoid ABCD undergoes some different transformations.

Question

Determine which transformations listed below result in a congruent trapezoid, A'B'C'D'.

Drag each transformation on the left to indicate whether it is either congruent or not congruent to ABCD.

Choices

A translation of 6 units down and 3 units to the right
A dilation by a factor of 2, centered at the origin
A 180o rotation counterclockwise about the origin
A reflection across the y-axis
Answers

Congruent to ABCD
Not Congruent to ABCD

Answer 1

To determine whether the transformations result in a congruent trapezoid A'B'C'D', we analyze each transformation one by one:

1. A translation of 6 units down and 3 units to the right:

   • Congruent to ABCD.
   • Translations preserve the shape and size of the figure.

2. A dilation by a factor of 2, centered at the origin:

   • Not Congruent to ABCD.
   • Dilation changes the size of the figure, hence creating a similar figure, but not congruent.

3. A 180° rotation counterclockwise about the origin:

   • Congruent to ABCD.
   • Rotations preserve the shape and size of figures.

4. A reflection across the y-axis:

   • Congruent to ABCD.
   • Reflections also preserve the shape and size of figures.

So, the classifications are as follows:

• A translation of 6 units down and 3 units to the right: Congruent to ABCD
• A dilation by a factor of 2, centered at the origin: Not Congruent to ABCD
• A 180° rotation counterclockwise about the origin: Congruent to ABCD
• A reflection across the y-axis: Congruent to ABCD