Since, the coordinates of the midpoint of line GH are M[tex](\frac{-13}{2}, -6)[/tex].
The coordinates of endpoint G are (-4,1)
We have to determine the coordinates of endpoint H.
The midpoint of the line segment joining the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by the formula [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex].
Here, The endpoint G is (-4,1) So, [tex]x_1 = -4 , y_1=1[/tex]
Let the endpoint H be [tex](x_2,y_2)[/tex]
The midpoint coordinate M is [tex](\frac{-13}{2}, -6)[/tex].
So, [tex]\frac{-13}{2} = \frac{-4+x_2}{2}[/tex]
[tex]{-13} = {-4+x_2}[/tex]
[tex]{-13}+4 = {x_2}[/tex]
[tex]{x_2}=9[/tex]
Now, [tex]-6 = \frac{1+y_2}{2}[/tex]
[tex]-12 = {1+y_2}[/tex]
[tex]y_2= -13[/tex]
So, the other endpoint H is (-9,-13).
