Final answer:
To find the coordinates of point B, we can use the midpoint formula: (7 + x)/2 = 2 and (-1 + y)/2 = 1.
Solving for x and y, we find that the coordinates of point B are (-3, 3).
Step-by-step explanation:
The midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates of its endpoints.
Given that the midpoint is (2, 1) and endpoint A is (7, -1), we can set up the following equation:
(7 + x)/2 = 2 and (-1 + y)/2 = 1
Simplifying these equations, we get:
7 + x = 4 and -1 + y = 2
Solving for x and y, we find:
x = -3 and y = 3
Therefore, the coordinates of point B are (-3, 3).