By definition, the formula to find a Midpoint is:
[tex]M=(\frac{x_1+x_2}{2}+\frac{y_2-y_1}{2})[/tex]
Where the coordinates of the first point are:
[tex](x_1,y_1)[/tex]
And the coordinates of the second point is:
[tex](x_2,y_2)[/tex]
Let be the coordinates of the Midpoint:
[tex](x_M,y_M)[/tex]
In this case, knowing coordinates of the point A and the Midpoint, you can set up the following equations:
- Equation 1:
[tex]x_M=\frac{x_A+x_B}{2}[/tex]
- Equation 2:
[tex]y_M=\frac{y_A+y_B}{2}[/tex]
Choose the Equation 1, substiutute values and solve for x-coordinate of the endpoint B:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ \\ 2=\frac{-3+x_B}{2} \\ \\ (2)(2)=-3+x_B \\ 4+3=x_B \\ x_B=7 \end{gathered}[/tex]
Now choose the Equation 2 and solve for the y-coordinate of the point B:
[tex]\begin{gathered} y_M=\frac{y_A+y_B}{2} \\ \\ -1=\frac{-5+y_B}{2} \\ \\ (-1)(2)=-5+y_B \\ -2+5=y_B \\ y_B=3 \end{gathered}[/tex]
Therefore, the coordinates of P are:
[tex]B(7,3)[/tex]
