Final answer:
To find the coordinates of point B, you use the midpoint formula with provided coordinates of A and M. By solving the resulting system of equations, you determine that the coordinates of B are (2, 3).
Step-by-step explanation:
To find the coordinates of point B when you know that point M is the midpoint of AB, and you have the coordinates of A (-8, 1) and M (-3, 2), you can use the midpoint formula, which states that the coordinates of the midpoint M are given by:
M = ((x1 + x2) / 2, (y1 + y2) / 2).
Where (x1, y1) are the coordinates of A and (x2, y2) are the coordinates of B. Since M is the midpoint, you can plug in the known values and set up a system of equations to find x2 and y2.
The equations will be:
- -3 = (-8 + x2) / 2
- 2 = (1 + y2) / 2
By solving these equations, we find that:
- x2 = -3 × 2 + 8 = 2
- y2 = 2 × 2 - 1 = 3
Therefore, the coordinates of point B are (2, 3).