Question

Which of the following sequence of transformations relates all the four triangles in the figure given below?

• A. $JKL\stackrel{\text{Reflection along the x-axis}}{\to }ACB\stackrel{\text{Reflection along the y-axis}}{\to }DEF\stackrel{\text{Reflection along the y-axis}}{\to }GHI$
• B. $ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the x-axis}}{\to }DEF$
• C. $DEF\stackrel{\text{Reflection along the y-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the y-axis}}{\to }ACB$
• D. $GHI\stackrel{\text{Reflection along the y-axis}}{\to }DEF\stackrel{\text{Reflection along the y-axis}}{\to }ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL$

Answer 1

The correct option is B $ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the x-axis}}{\to }DEF$

We will check all the options one-by-one to get the correct sequence of transformations that relates all the four triangles.

In option A:
$DEF\stackrel{\text{Reflection along the y-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the y-axis}}{\to }ACB$


The above image shows the reflection of $DEF$ along the y-axis that produces image $ACB$ and not $JKL$ as given in the option.


The above image shows the reflection of $JKL$ along the y-axis that produces the image $GHI$.


The above image shows the reflection of $GHI$ along the y-axis, which produces the image $JKL$ and not $ACB$ as given in the option.
This sequence produces one correct image and two incorrect images obtained after the transformations.
Thus, this sequence is incorrect.

In option B:$GHI\stackrel{\text{Reflection along the y-axis}}{\to }DEF\stackrel{\text{Reflection along the y-axis}}{\to }ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL$

The above image shows the reflection of $GHI$ along the y-axis, which produces the image $JKL$ and not $DEF$ as given in the option.


The above image shows the reflection of $DEF$ along the y-axis that produces the image $ACB$.


The above image shows the reflection of $ACB$ along the x-axis which produces the image $JKL$.

This sequence produces two correct images and one incorrect image obtained after the transformations.
Thus, this sequence is incorrect.

In option C : $JKL\stackrel{\text{Reflection along the x-axis}}{\to }ACB\stackrel{\text{Reflection along the y-axis}}{\to }DEF\stackrel{\text{Reflection along the y-axis}}{\to }GHI$

The above image shows the reflection of $JKL$ along the x-axis that produces the image $ACB$.


The above image shows the reflection of $ACB$ along the y-axis that produces the image $DEF$.


The above image shows the reflection of $DEF$ along the y-axis that produces the image $ACB$ and not $GHI$.
This sequence produces two correct images and one incorrect image obtained after the transformations.
Thus, this sequence is incorrect.

In option D: $ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the x-axis}}{\to }DEF$

The above image shows the reflection of $ACB$ along the x-axis that produces the image $JKL$.


The above image shows the reflection of $JKL$ along the y-axis that produces the image $GHI$.


The above image shows the reflection of $GHI$ along the x-axis that produces the image $DEF$.
This sequence produces all three correct images obtained after the transformations.
Thus, this sequence is correct.

➡Option D is correct.