The coordinates of endpoint B are:
[tex]\boxed{x_{2}=6} \\ \\ \boxed{y_{2}=-9}[/tex]
And point B is:
[tex]\boxed{B(6,-9)}[/tex]
The midpoint formula is expressed as follows:
[tex]For \ two \ endpoints \ (x_{1},y_{1}) \ and \ (x_{2},y_{2}): \\ \\ M(x,y)=M\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right) \\ \\ \\ Here \ one \ endpoint \ is: \\ \\ A(x_{1},y_{1})=A(2, -3) \\ \\ \\ And \ the \ midpoint \ is: \\ \\ M(x,y)=M(4, -6) \\ \\ \\ So: \\ \\ \bullet x=\frac{x_{1}+x_{2}}{2} \\ \\ Substituting \ values: \\ \\ 4=\frac{2+x_{2}}{2} \\ \\ Isolating \ x_{2}: \\ \\ 2+x_{2}=8 \\ \\ x_{2}=8-2 \\ \\ x_{2}=6[/tex]
[tex]\bullet y=\frac{y_{1}+y_{2}}{2} \\ \\ Substituting \ values: \\ \\ -6=\frac{-3+y_{2}}{2} \\ \\ Isolating \ y_{2}: \\ \\ -3+y_{2}=-12 \\ \\ x_{2}=-12+3 \\ \\ y_{2}=-9[/tex]
So the coordinates of endpoint B are:
[tex]\boxed{x_{2}=6} \\ \\ \boxed{y_{2}=-9}[/tex]
And point B is:
[tex]\boxed{B(6,-9)}[/tex]
Midpoint: https://brainly.com/question/13773601
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