Question

composing transformations
which figure represents the final image after composition $r_{y - axis}circ t_{3,-1}$ is applied to rectangle lmnp?

Explanation:

Step1: Understand the transformations

$T_{3,-1}$ is a translation 3 units to the right and 1 unit down. $r_{y - axis}$ is a reflection over the y - axis.

Step2: First apply the translation

For a point $(x,y)$ on rectangle LMNP, after translation $T_{3,-1}$, the new point is $(x + 3,y-1)$.

Step3: Then apply the reflection

After reflection $r_{y - axis}$ on the point $(x + 3,y - 1)$, the new point is $(-(x + 3),y - 1)=(-x-3,y - 1)$.
Let's assume a vertex of rectangle LMNP is $(x_0,y_0)$. After $T_{3,-1}$ it becomes $(x_0 + 3,y_0-1)$, and after $r_{y - axis}$ it becomes $(-x_0 - 3,y_0-1)$.
If we consider the general effect on the rectangle's position and orientation, we can analyze the net change.
The translation moves the rectangle to the right and down, and the reflection flips it across the y - axis.
By visualizing or applying the transformations to key points (vertices) of rectangle LMNP, we can determine the final image.

Answer:

(Without seeing the actual visual options clearly, we can't give a specific numbered answer. But the above steps show how to find the final image.)