<u>ANSWER:</u>
The midpoint of AB is M(-5,1). The coordinates of B are (-6, 7)
<u>SOLUTION:
</u>
Given, the midpoint of AB is M(-5,1).
The coordinates of A are (-4,-5),
We need to find the coordinates of B.
We know that, mid-point formula for two points A
and B
is given by
![M\left(x_{3}, y_{3}\right)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)](https://tex.z-dn.net/?f=M%5Cleft%28x_%7B3%7D%2C%20y_%7B3%7D%5Cright%29%3D%5Cleft%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
Here, in our problem, ![\mathrm{x}_{3}=-5, \mathrm{y}_{3}=1, \mathrm{x}_{1}=-4 \text { and } \mathrm{y}_{1}=-5](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%7D_%7B3%7D%3D-5%2C%20%5Cmathrm%7By%7D_%7B3%7D%3D1%2C%20%5Cmathrm%7Bx%7D_%7B1%7D%3D-4%20%5Ctext%20%7B%20and%20%7D%20%5Cmathrm%7By%7D_%7B1%7D%3D-5)
Now, on substituting values in midpoint formula, we get
![(-5,1)=\left(\frac{-4+x_{2}}{2}, \frac{-5+y_{2}}{2}\right)](https://tex.z-dn.net/?f=%28-5%2C1%29%3D%5Cleft%28%5Cfrac%7B-4%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7B-5%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
On comparing, with the formula,
![\frac{-4+x_{2}}{2}=-5 \text { and } \frac{-5+y_{2}}{2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B-4%2Bx_%7B2%7D%7D%7B2%7D%3D-5%20%5Ctext%20%7B%20and%20%7D%20%5Cfrac%7B-5%2By_%7B2%7D%7D%7B2%7D%3D1)
![-4+\mathrm{x}_{2}=-10 \text { and }-5+\mathrm{y}_{2}=2](https://tex.z-dn.net/?f=-4%2B%5Cmathrm%7Bx%7D_%7B2%7D%3D-10%20%5Ctext%20%7B%20and%20%7D-5%2B%5Cmathrm%7By%7D_%7B2%7D%3D2)
![\mathrm{x}_{2}=-6 \text { and } \mathrm{y}_{2}=7](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%7D_%7B2%7D%3D-6%20%5Ctext%20%7B%20and%20%7D%20%5Cmathrm%7By%7D_%7B2%7D%3D7)
Hence, the coordinates of b are (-6, 7).