6
Question
Which of the following sequence of transformations relates all the four triangles in the figure given below?
Which of the following sequence of transformations relates all the four triangles in the figure given below?
Open in App
Solution
The correct option is B ACBReflection along the x-axis−−−−−−−−−−−−−−−→JKLReflection along the y-axis−−−−−−−−−−−−−−−→GHIReflection along the x-axis−−−−−−−−−−−−−−−→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:
DEFReflection along the y-axis−−−−−−−−−−−−−−−→JKLReflection along the y-axis−−−−−−−−−−−−−−−→GHIReflection along the y-axis−−−−−−−−−−−−−−−→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:GHIReflection along the y-axis−−−−−−−−−−−−−−−→DEFReflection along the y-axis−−−−−−−−−−−−−−−→ACBReflection along the x-axis−−−−−−−−−−−−−−−→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 : JKLReflection along the x-axis−−−−−−−−−−−−−−−→ACBReflection along the y-axis−−−−−−−−−−−−−−−→DEFReflection along the y-axis−−−−−−−−−−−−−−−→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: ACBReflection along the x-axis−−−−−−−−−−−−−−−→JKLReflection along the y-axis−−−−−−−−−−−−−−−→GHIReflection along the x-axis−−−−−−−−−−−−−−−→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.
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:
DEFReflection along the y-axis−−−−−−−−−−−−−−−→JKLReflection along the y-axis−−−−−−−−−−−−−−−→GHIReflection along the y-axis−−−−−−−−−−−−−−−→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:GHIReflection along the y-axis−−−−−−−−−−−−−−−→DEFReflection along the y-axis−−−−−−−−−−−−−−−→ACBReflection along the x-axis−−−−−−−−−−−−−−−→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 : JKLReflection along the x-axis−−−−−−−−−−−−−−−→ACBReflection along the y-axis−−−−−−−−−−−−−−−→DEFReflection along the y-axis−−−−−−−−−−−−−−−→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: ACBReflection along the x-axis−−−−−−−−−−−−−−−→JKLReflection along the y-axis−−−−−−−−−−−−−−−→GHIReflection along the x-axis−−−−−−−−−−−−−−−→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.
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
