The problem asks us to determine the sequence of transformations that would map Figure M onto Figure N, based on the given options: a rotation of 90 degrees clockwise about the origin, followed by a translation down.

1. Problem Description

The problem asks us to determine the sequence of transformations that would map Figure M onto Figure N, based on the given options: a rotation of 90 degrees clockwise about the origin, followed by a translation down.

2. Solution Steps

First, we consider the rotation of Figure M by 90 degrees clockwise about the origin. A 90 degree clockwise rotation about the origin transforms a point $(x, y)$ to $(y, -x)$.

Let's estimate the coordinates of the vertices of Figure M. Approximate coordinates are (7, 2), (9, 0), (8, 4).

Rotating these points 90 degrees clockwise gives us:

(7, 2) -> (2, -7)

(9, 0) -> (0, -9)

(8, 4) -> (4, -8)

These points appear to roughly match the orientation of Figure N. The vertices of Figure N are near (2, -7), (0, -9), and (4, -8).

Therefore, the rotation is correct.

Next, let's analyze the translation. Visually, Figure N is below the rotated image. Therefore, a translation "down" seems appropriate. To see how much, compare the vertices of Figure N to the rotated points. It appears a translation of zero units is adequate since they roughly coincide.

3. Final Answer

A rotation of 90 degrees clockwise about the origin followed by a translation down 0 units.