To find the midpoint of the line segment connecting points A and B given by the coordinates A(2,-2) and B(6,5), you use the midpoint formula, which is \((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\).
In this case, the x-coordinates of points A and B are 2 and 6, respectively. So, calculating the midpoint for the x-coordinates:
\[ \frac{2 + 6}{2} = \frac{8}{2} = 4 \]
Next, for the y-coordinates of points A and B, which are -2 and 5:
\[ \frac{-2 + 5}{2} = \frac{3}{2} = 1.5 \]
Thus, the midpoint M of line segment AB is at the coordinates (4, 1.5).
Now, considering the options given:
- A. It finds the sole midpoint of points A and B: This is true, but it lacks specificity on how it applies to the calculations in your question.
- B. It finds the average distance between the two x-values of points A and B: This is not correct; it finds the average of the x-coordinates, not the distance.
- C. It finds the distance between points A and B: This is incorrect; it does not give the distance between the two points.
- D. It finds the average distance between the two y-values of points A and B: This is similarly incorrect; it finds the average of the y-coordinates.
The correct choice, if looking for how to arrive at the midpoint, would most closely match option A, as that is what the calculations ultimately accomplish. However, it should be emphasized that the values derived from averaging the x-coordinates and y-coordinates result in identifying the midpoint itself, not an average distance.