Respuesta :
Given:
The midpoint of AB is M
Coordinates of M (0,-4)
Coordinates of A (2.-1)
Find-:
The value of coordinates of B
Explanation-:
The Coordinates of B
Let Coordinates of B is
[tex]B=(x,y)[/tex]The midpoint formula is
[tex]M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where,
[tex]\begin{gathered} (x,y)=\text{ Midpoint} \\ \\ (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}[/tex]The midpoint is
[tex]\begin{gathered} M=(0,-4) \\ \\ A=(2,-1) \\ \\ B=(x,y) \end{gathered}[/tex]So, Midpoint is
[tex]\begin{gathered} (0,-4)=(\frac{2+x}{2},\frac{-1+y}{2}) \\ \\ \end{gathered}[/tex]So, the (x,y) is
[tex]\begin{gathered} \frac{2+x}{2}=0 \\ \\ 2+x=0 \\ \\ x=-2 \end{gathered}[/tex]The value of "y"
[tex]\begin{gathered} \frac{-1+y}{2}=-4 \\ \\ -1+y=-4\times2 \\ \\ -1+y=-8 \\ \\ y=-8+1 \\ \\ y=-7 \end{gathered}[/tex]So the point B is
[tex]B(x,y)=(-2,-7)[/tex]