ANSWER:
The midpoint of AB is M(-5,1). The coordinates of B are (-6, 7)
SOLUTION:
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[tex](x_{1}, y_{1})[/tex] and B [tex](x_{1}, y_{2})[/tex] is given by
[tex]M\left(x_{3}, y_{3}\right)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here, in our problem, [tex]\mathrm{x}_{3}=-5, \mathrm{y}_{3}=1, \mathrm{x}_{1}=-4 \text { and } \mathrm{y}_{1}=-5[/tex]
Now, on substituting values in midpoint formula, we get
[tex](-5,1)=\left(\frac{-4+x_{2}}{2}, \frac{-5+y_{2}}{2}\right)[/tex]
On comparing, with the formula,
[tex]\frac{-4+x_{2}}{2}=-5 \text { and } \frac{-5+y_{2}}{2}=1[/tex]
[tex]-4+\mathrm{x}_{2}=-10 \text { and }-5+\mathrm{y}_{2}=2[/tex]
[tex]\mathrm{x}_{2}=-6 \text { and } \mathrm{y}_{2}=7[/tex]
Hence, the coordinates of b are (-6, 7).
