Question

What transformations $△ABC$ require to join with $△EDF$ to form a rectangle?

• A. Rotation, reflection
• B. Translation, dilation
• C. Translation, rotation
• D. Reflection, translation

Answer 1

The correct option is C Translation, rotation

Rotation ${90}^o$ clockwise about the origin changes the quadrant and also rotates the image. Reflection on the $y$-axis changes the orientation and also the quadrant of the image. As both of them change the quadrant of the image, it is not possible to keep the resultant image in the second quadrant. Hence, option B is incorrect.

Translation changes either or both $x$ and $y$-coordinates. Dilation changes the size of the image. There is a change in the size of the resultant image. Hence, option C is incorrect.

Reflection changes the orientation and also the quadrant of the image. Translation changes either or both $x$ and $y$-coordinates. As there is no rotation, it is not possible to get the resultant image. Hence, option D is not correct.

For Option A with translation and rotation:
Step 1: Translation of two units toward the right and then two units up
Step 2: Rotation of ${90}^o$ counterclockwise about the origin

Hence, the correct answer is option A.