Question

retake bell work (lesson quiz savvas)
use the graph of two triangles for items 1 and 2.
in the graph, ( \triangle pqrcong\triangle stu ). complete the statement below to describe a composition of rigid transformations that maps

reflect ( \triangle pqr ) across the line ( y=square ). then translate the resulting image ( square ) units to the right.

Explanation:

Step1: Analyze the reflection line

To find the line of reflection, observe the vertical relationship between corresponding points. The mid - point of \(Q( - 1,6)\) and \(T(1, - 6)\) (or \(R(0,3)\) and \(U(2, - 3)\) or \(P( - 5,2)\) and \(S(0,2)\)) for the \(y\) - coordinate.
The formula for the mid - point of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). For \(P( - 5,2)\) and \(S(0,2)\), the line of reflection is \(y = 2\) (since the \(y\) - coordinate of the mid - point of \(P\) and \(S\) is \(y=\frac{2 + 2}{2}=2\)).

Step2: Analyze the translation

After reflection across \(y = 2\), count the horizontal distance between a point (say the reflected point of \(P\)) and its corresponding point in \(\triangle STU\).
Take point \(P(-5,2)\). After reflection across \(y = 2\), it remains \(P'(-5,2)\). The \(x\) - coordinate of \(P'\) is \(-5\) and the \(x\) - coordinate of \(S\) (a corresponding point) is \(0\). The number of units of translation to the right is \(0-(-5)=5\).

Answer:

Reflect \(\triangle PQR\) across the line \(y = 2\). Then translate the resulting image \(5\) units to the right.