EXPLANATION :
From the problem, we have segment GH and the midpoint is M(-2, 5).
One of the endpoints has coordinates of H(-3, 7)
and we need to find the coordinates of G(x, y)
The midpoint formula is :
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) are the coordinates of G
(x2, y2) = (-3, 7) are the coordinates of H
and (-2, 5) are the coordinates of the midpoint.
Then :
[tex](-2,5)=(\frac{x+(-3)}{2},\frac{y+7}{2})[/tex]We can equate the x coordinate :
[tex]\begin{gathered} -2=\frac{x+(-3)}{2} \\ \\ \text{ cross multiply :} \\ -2(2)=x-3 \\ -4=x-3 \\ -4+3=x \\ -1=x \\ x=-1 \end{gathered}[/tex]then the y coordinate :
[tex]\begin{gathered} 5=\frac{y+7}{2} \\ \\ \text{ cross multiply :} \\ 5(2)=y+7 \\ 10=y+7 \\ 10-7=y \\ 3=y \\ y=3 \end{gathered}[/tex]Now we have the point (-1, 3)
ANSWER :
The coordinates of the other endpoint are G(-1, 3)
