Question

triangle rst was transformed using the rule (x,y)→(−x,−y). the vertices of the triangles are shown. r (1,1) r (-1,-1) s (3,1) s (-3,-1) t (1,6) 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.

Explanation:

Step1: Recall rotation rules

For a 90° rotation about the origin, $(x,y)\to(-y,x)$.

Step2: Analyze 180° rotation

For a 180° rotation about the origin, $(x,y)\to(-x,-y)$. Given the rule $(x,y)\to(-x,-y)$ and the vertices transformation (e.g., $R(1,1)\to R'(-1,-1)$), it matches 180° rotation rule.

Step3: Check other rotation rules

For a 270° rotation about the origin, $(x,y)\to(y, - x)$. For a 360° rotation about the origin, $(x,y)\to(x,y)$. So, it's a 180° rotation.

Answer:

B. The transformation was a 180° rotation about the origin.