Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

Question

R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Which best describes the transformation?

The transformation was a 90° rotation about the origin.
The transformation was a 180° rotation about the origin.
The transformation was a 270° rotation about the origin.
The transformation was a 360° rotation about the origin.

Answer 1

The transformation given by the rule \((x, y) \to (-x, -y)\) represents a 180° rotation about the origin. This is because each point is moved to the position that is diametrically opposite relative to the origin.

To confirm, we can look at the transformed coordinates of the vertices:

• \( R(1, 1) \) transforms to \( R'(-1, -1) \)
• \( S(3, 1) \) transforms to \( S'(-3, -1) \)
• \( T(1, 6) \) transforms to \( T'(-1, -6) \)

Each point is indeed rotated 180° about the origin.

Thus, the correct answer is:

The transformation was a 180° rotation about the origin.