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

A $90^{\circ}$ rotation about the origin has the rule $(x,y)\to(-y,x)$. A $180^{\circ}$ rotation about the origin has the rule $(x,y)\to(-x,-y)$. A $270^{\circ}$ rotation about the origin has the rule $(x,y)\to(y, - x)$. A $360^{\circ}$ rotation about the origin has the rule $(x,y)\to(x,y)$.

Step2: Match the given rule

The given transformation rule is $(x,y)\to(-x,-y)$, which matches the rule for a $180^{\circ}$ rotation about the origin.

Answer:

The transformation was a $180^{\circ}$ rotation about the origin.