To find the area of a triangle, we'll need the base and height. Since (-4, -3) and (5, -3) have the same y-coordinate, the line between them is parallel to the x-axis. This makes it relatively easy to work with. The distance between the two points is 5 - (-4) = 9. Let's call that the base.
The height, then, must be perpendicular to the base, and parallel to the y-axis. The third point is located at (-2, -7). Place a point on the base at (-2, -3), and the resulting line between (-2, -7) and (-2, -3) is the height of the triangle. The distance of that line is the difference between -7 and -3, or 4.
Since b = 9 and h = 4, the area, (1/2)(b)(h), is 18, choice (D).