Question

Which of the following sequence of transformations has been used to obtain the image $EFGH\text{if}ABCD$ is the preimage? Is figure $EFGH$ congruent to $ABCD?$

• A. Clockwise rotation of ${270}^{\circ }$ and rightward translation by $1$ unit, Yes
• B. Reflection along the y-axis and rightward translation by $1$ unit, Yes
• C. Reflection along the y-axis and leftward translation by $2$ units, No
• D. Clockwise rotation of ${180}^{\circ }$ and reflection along the y-axis, No

Answer 1

The correct option is B Reflection along the y-axis and rightward translation by $1$ unit, Yes

In option A: Reflection along the y-axis and rightward translation by $1$ unit, Yes
Let’s visualize the transformation step-by-step to get the image.

1. The image given below shows the reflection of $ABCD$ along the y-axis to obtain image $EFGH.$


2. The image given below shows the translation of the reflected image (shown using dotted lines) by $1$ unit in the right direction.


Now, $EFGH$ is the same as the desired image asked in the question.
Thus, reflection along the y-axis and translation of $1$ unit in the right direction will be the correct sequence of transformation used to obtain $EFGH$ from $ABCD$.

Also, since reflection and translation are rigid transformations and rigid transformations always produce congruent figures, $EFGH$ will be congruent to $ABCD$.

In option B: Reflection along the y-axis and leftward translation by $2$ units, No
Let’s visualize the transformation step-by-step:

1. The image given below shows the reflection of $ABCD$ along the y-axis to obtain image $EFGH$.


2. The image given below shows the translation of the reflected image (shown using dotted lines) by $2$ units toward the left.


Now, $EFGH$ is not the same as the desired image asked in the question; therefore, this transformation is not correct.

In option C: Clockwise rotation of ${180}^{\circ }$ and reflection along the y-axis, No
Let’s visualize the transformation step-by-step:


The above image shows the clockwise rotation of $ABCD$ by ${180}^{\circ }$ to get $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ , and then its reflection along the y-axis to get the final image $EFGH$.

If we closely observe the image here, we can see that the coordinate $E$ of the above image is not matching with the coordinate $E$ of the image asked in the question, which means that the orientations are not the same.
Therefore, this transformation is not correct.

In option D: Clockwise rotation of ${270}^{\circ }$ and rightward translation by $1$ unit, Yes
Let’s visualize the transformation step-by-step.


The above image shows the clockwise rotation of $ABCD$ by ${270}^{\circ }$ and then its rightward translation by 1 unit.
If we observe the image here, we can see that $EFGH$ is not the same as what is asked in the question.
Thus, this transformation is not correct.

➡Option A is correct.