The problem asks us to determine a series of transformations that would map Figure M onto Figure N. The available options are reflection, rotation, and translation.

1. Problem Description

The problem asks us to determine a series of transformations that would map Figure M onto Figure N. The available options are reflection, rotation, and translation.

2. Solution Steps

First, observe the orientation of Figure M and Figure N. It appears that Figure N is a reflection of Figure M across the x-axis or a horizontal line.

To verify, we can reflect Figure M across the x-axis. Let's assume the vertices of Figure M are approximately at (8, -1), (10, -3), and (7, -4). Reflecting these points across the x-axis would result in (8, 1), (10, 3), and (7, 4). This reflection does not appear to match the position of Figure N.

Let's consider a reflection across a horizontal line, which is equivalent to a reflection about the x-axis followed by a translation in the y-direction.

If we reflect figure M across the x-axis, the y-coordinates change sign. Then, we need to translate to align the reflected image with Figure N.

Observe the approximate coordinates of figure N. Its vertices are at (8, -7), (10, -5), and (7, -4).

If we reflect figure M about the x-axis, we get (8, 1), (10, 3), (7, 4) for the vertices.

Let's analyze the coordinates:

Figure M: (8,-1), (10,-3), (7,-4)

Figure N: (8,-7), (10,-5), (7,-4)

Reflection across x-axis of Figure M: (8,1), (10,3), (7,4)

To map the reflection of Figure M onto Figure N, we need to translate the reflection down by 8 units. (i.e., (8, 1) -> (8, -7)).

(10, 3) -> (10, -5) which also corresponds to a translation of -8 units.

(7, 4) -> (7, -4) which corresponds to a translation of -8 units.

So, we need a reflection followed by a translation.

3. Final Answer

Reflection followed by a translation.