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Compositions of Transformations Quick Check

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Question
Use the image to answer the question.

Two quadrilaterals, upper A upper B upper C upper D and upper E upper F upper G upper H, are graphed on a coordinate plane. The x-axis ranges from negative 7 to 7 in increments of 1. The y-axis ranges from negative 3 to 8 in increments of 1.

Assess parallelograms ADCB and EHGF to decide if they are congruent.

(1 point)
Responses

Yes, ADCB≅EHGF because parallelogram ADCB was reflected.
Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was reflected.

Yes, ADCB≅EHGF since parallelogram ADCB was translated.
Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F since parallelogram upper A upper D upper C upper B was translated.

No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.
No, upper A upper D upper C upper B is not congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was dilated.

Yes, ADCB≅EHGF because parallelogram ADCB was rotated.

1 answer

To determine whether the parallelograms ADCB and EHGF are congruent, we need to consider the types of transformations involved. Congruent figures can be achieved through rigid transformations like reflections, translations, and rotations, but not through dilations, which change the size of a shape.

Given the options:

  1. "Yes, ADCB≅EHGF because parallelogram ADCB was reflected."
  2. "Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was reflected."
  3. "Yes, ADCB≅EHGF since parallelogram ADCB was translated."
  4. "Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F since parallelogram upper A upper D upper C upper B was translated."
  5. "No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated."
  6. "No, upper A upper D upper C upper B is not congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was dilated."
  7. "Yes, ADCB≅EHGF because parallelogram ADCB was rotated."

Without the image, the best way to choose the correct response is based on common transformations. If ADCB was either reflected, translated, or rotated to get to EHGF, they would be congruent. If there was a dilation involved, they would not be congruent.

If you know any specifics about the transformations that occurred, please provide that information, and I can help you select the correct answer. However, based on the options provided:

  • If ADCB was reflected, translated, or rotated to result in EHGF, options 1, 2, 3, 4, or 7 would apply.
  • If there was a dilation, options 5 or 6 would apply and indicate that they are not congruent.

Please check back to confirm the transformations to make an accurate choice.