Question

Which transformation will the preimage $ABCD$ undergo to obtain the image $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }?$

• A. Reflection
• B. Translation
• C. Dilation
• D. Rotation

Answer 1

The correct option is B Translation

There is no change in the orientation of the square that can be observed. So, reflection and rotation cannot be possible.
Since there is no change in size, this could be dilation about the origin with a scale factor of 1 or -1. But the position of the image and preimage are different. So, this cannot be dilation with scale factor 1. Also, the orientation of the preimage is the same as that of the image. So, this cannot be dilation with scale factor -1. Hence, option c is not the correct answer.

(Vertex A translating to form A')

(Vertex B translating to form B')

(Vertex C translating to form C')

(Vertex D translating to form D')

Observing each of the vertices of the square, we can say that the vertices have been shifted toward the left by $4$ units and also $6$ units up to form the image $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$. So, the transformation involved in moving the preimage $ABCD$ to form the image $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ is translation.