The grid shows Figure Q and its image Figure Q′ after a transformation. Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent?

Question

The grid shows Figure Q and its image Figure Q′ after a transformation.

Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent?

1.  Clockwise rotation of 180° about the origin 
2. Counterclockwise rotation of 90° about the origin 
3. Clockwise rotation of 90° about the origin 
4. Counterclockwise rotation of 270° about the origin

Answer 1

A counterclockwise 180^o rotation about the origin results in the same location as a clockwise 180^o rotation about the origin: 2 quadrants ahead of the current location (which is the same as 2 quadrants back from the current location).

A 90^o clockwise rotation about the origin results in the same location as a 270^o counterclockwise direction: one quadrant clockwise from the current location (which is the same location as three quadrants counterclockwise from the present location).

A 90^o counterclockwise rotation about the origin results in the same location as a 270^o clockwise direction: one quadrant counterclockwise from the current location (which is the same location as three quadrants clockwise from the present location).

In this problem, the image was rotated about the origin one quadrant counterclockwise from the pre-image location (or, equivalently, three quadrants clockwise around the origin from the pre-image). So, the correct answer choice is (2).

Answer 2

Rotate Q 90° counterclockwise about the origin to obtain Q'.