The midpoint of Line AB is M(3, 3). The co-ordinates of B are (4, 7)
Solution:
Given that, the midpoint of Line AB is M(3, 3)
And the coordinates of A are (2, -1)
We have to find what are the coordinates of B
[tex]\text { The midpoint of a line } A\left(x_{1}, y_{1}\right) \text { and } B\left(x_{2}, y_{2}\right) \text { is given by } M=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{2}+y_{2}}{2}\right)[/tex]
[tex]\text { Here } \mathrm{M}=(3,3) \text { and } \mathrm{A}\left(x_{1}, y_{1}\right)=(2,-1) \text { and } B\left(x_{2}, y_{2}\right)=?[/tex]
Substituting the values we get,
[tex](3,3)=\left(\frac{2+x_{2}}{2}, \frac{-1+y_{2}}{2}\right)[/tex]
[tex]\text { Now, by comparison, } \frac{2+x_{2}}{2}=3 \text { and } \frac{-1+y_{2}}{2}=3[/tex]
[tex]\begin{array}{l}{\rightarrow 2+x_{2}=6 \text { and }-1+y_{2}=6} \\\\ {\rightarrow x_{2}=6-2 \text { and } y_{2}=6+1} \\\\ {\rightarrow x_{2}=4 \text { and } y_{2}=7}\end{array}[/tex]
Hence, the co – ordinates of B is (4, 7)
