Question

in the graph, \\( \triangle pqr \cong \triangle stu \\).

choose the words that complete the statement to describe a composition of rigid motions that maps \\( \triangle pqr \\) to \\( \triangle stu \\).

reflect \\( \triangle pqr \\) across the line

then translate the resulting image
units to the right.

Explanation:

Step1: Reflect across \(y = 0\)

Reflecting a point \((x,y)\) across the line \(y = 0\) (the \(x -\)axis) gives the point \((x,-y)\). For example, if \(P(x_1,y_1)\) is a vertex of \(\triangle PQR\), its image after reflection across \(y = 0\) is \(P'(x_1,-y_1)\).

Step2: Translate

After reflecting \(\triangle PQR\) across \(y = 0\), we need to translate the resulting image. Count the horizontal distance from the reflected triangle (after reflection across \(y = 0\)) to \(\triangle STU\). The horizontal translation is \(2\) units to the right.

Answer:

Reflect \(\triangle PQR\) across the line \(y = 0\). Then translate the resulting image \(2\) units to the right.