IF M(3-1) is the midpoint of the segment AB and A(8.12) is the coordinates of A. Fin the coordinates of point B.

Note that A(8,12)+(-5,-13) = M(3,-1)

Since M is halfway to B, we need to add the same amounts to M that got us there from A:
M(3,-1)+(-5,-13) = B(-2,-14)

To find the coordinates of point B, we need to know the coordinates of point A and the midpoint M.

Let's break down the problem step by step:

1. Given the midpoint M(3, -1) and the coordinates of point A (8, 12).
2. The midpoint of a line segment is the average of the coordinates of its endpoints. So, we can set up the following equation to find the x-coordinate of point B:

(x-coordinate of A + x-coordinate of B) / 2 = x-coordinate of M

Substituting the given values:

(8 + x-coordinate of B) / 2 = 3

3. Solving the equation:

8 + x-coordinate of B = 6

x-coordinate of B = 6 - 8 = -2

4. Now, let's find the y-coordinate of point B. Using the same logic as above, we set up the following equation:

(y-coordinate of A + y-coordinate of B) / 2 = y-coordinate of M

Substituting the given values:

(12 + y-coordinate of B) / 2 = -1

5. Solving the equation:

12 + y-coordinate of B = -2

y-coordinate of B = -2 - 12 = -14

6. Therefore, the coordinates of point B are (-2, -14).