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).