Final answer:
The locations of the points (-2, -7) and (2, 7) are related by being diagonal to each other since they are reflections over the origin with a slope of -1 when connected by a line. The correct answer is D) Diagonal.
Step-by-step explanation:
To understand how the locations of the points (-2, -7) and (2, 7) are related, we need to consider the properties of these two points in the Cartesian plane. First, let's examine the coordinates of these points. The first point (-2, -7) has both a negative x-coordinate and a negative y-coordinate, while the second point (2, 7) has both a positive x-coordinate and a positive y-coordinate. If we plot these points on a graph, they would be located in the third quadrant and the first quadrant, respectively.
Now, to find out the relation between these two points, we can observe that if we draw a line connecting the two points, the line will pass through the origin (0,0). This indicates that the line is diagonal, and since the x and y values of point (2,7) are both exactly the opposite of the x and y values of point (-2,-7), the line going through these points will also have a slope of negative one. The slope is found by the change in y divided by the change in x. For these points, it would be (7 - (-7)) / (2 - (-2)) which simplifies to 14/4 and gives a result of 3.5. However, the opposite signs of these coordinates reveal that they are reflections of each other across the origin, so the slope between any two such points is -1. This fact further supports that the correct answer to how these points are related is that they are diagonal to each other. Thus, the correct option in the final answer would be D) Diagonal.