Question

which function describes the transformation of \\( \triangle abn \\)?
\\( r _ { h } ( \triangle abn ) = \triangle n ^ { \prime } b ^ { \prime } a ^ { \prime } \\)
\\( r _ { h } ( \triangle abn ) = \triangle a ^ { \prime } b ^ { \prime } n ^ { \prime } \\)
\\( t _ { n n ^ { \prime } } ( \triangle abn ) = \triangle a ^ { \prime } b ^ { \prime } n ^ { \prime } \\)
\\( t _ { n n ^ { \prime } } ( \triangle abn ) = \triangle n ^ { \prime } b ^ { \prime } a ^ { \prime } \\)

Explanation:

Step1: Recall transformation definitions

Rotation \(R_h\) about line \(h\) changes the orientation of the figure. Translation \(T_{NN'}\) moves the figure without rotation.

Step2: Analyze the transformation

Since the figure is rotated about line \(h\) (not translated as there is no parallel shift), we consider rotation. When we rotate \(\triangle ABN\) about line \(h\), the order of vertices changes. The rotation of \(\triangle ABN\) about line \(h\) will map \(A\) to \(A'\), \(B\) to \(B'\) and \(N\) to \(N'\) in order. So \(R_h(\triangle ABN)=\triangle A'B'N'\)

Answer:

\(R_h(\triangle ABN)=\triangle A'B'N'\) (the second option)