Answer:
The coordinates of B is (-8,-5).
Step-by-step explanation:
The midpoint of line AB is M. The coordinate of M is (-6,-4).
The coordinates of A is (-4,-3)
We need to find the mid point of B.
If M(x,y) is the midpoint of the coordinates (x₁,y₁) and (x₂,y₂). The mid point theorem is used as follows :
![M(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})](https://tex.z-dn.net/?f=M%28x%2Cy%29%3D%28%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cdfrac%7By_1%2By_2%7D%7B2%7D%29)
Let the mid point of B is (x₂,y₂). Put (x,y) = (-6,-4), (x₁,y₁) = (-4,-3).
![(-6,-4)=(\dfrac{-4+x_2}{2},\dfrac{-3+y_2}{2})\\\\\dfrac{-4+x_2}{2}=-6\ \text{and}\ \dfrac{-3+y_2}{2}=-4\\\\-4+x_2=-12\ \text{and}\ -3+y_2=-8\\\\x_2=-12+4\ \text{and}\ y_2=-8+3\\\\x_2=-8\ \text{and}\ y_2=-5](https://tex.z-dn.net/?f=%28-6%2C-4%29%3D%28%5Cdfrac%7B-4%2Bx_2%7D%7B2%7D%2C%5Cdfrac%7B-3%2By_2%7D%7B2%7D%29%5C%5C%5C%5C%5Cdfrac%7B-4%2Bx_2%7D%7B2%7D%3D-6%5C%20%5Ctext%7Band%7D%5C%20%5Cdfrac%7B-3%2By_2%7D%7B2%7D%3D-4%5C%5C%5C%5C-4%2Bx_2%3D-12%5C%20%5Ctext%7Band%7D%5C%20-3%2By_2%3D-8%5C%5C%5C%5Cx_2%3D-12%2B4%5C%20%5Ctext%7Band%7D%5C%20y_2%3D-8%2B3%5C%5C%5C%5Cx_2%3D-8%5C%20%5Ctext%7Band%7D%5C%20y_2%3D-5)
So, the coordinates of B is (-8,-5).