Imagine you're moving along the segment. Since the midpoint is in the middle of the segment (obviously), it means that when you've traveled from G to A, you're halfway through your journey, along both x and y directions. So, let's break the problem in two and analyze both directions.
Along the x axis, you've moved from -3 to 1, so you moved 4 units forward. This means that you have 4 units still to go, and your journey will end at coordinate 5.
Similarly, along the y axis, you've moved from 5 to -4, so you moved 9 units downward. This means that you have 9 units still to go, and your journey will end at coordinate -13.
So, the coordinates of the endpoint are [tex] T = (5,-13) [/tex]
If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.
We have [tex] G = (-3, 5) [/tex] and [tex] T = (x_T,y_T) [/tex]. The midpoint is computed as
[tex] A = \left( \frac{-3+x_T}{2},\frac{5+y_T}{2} \right) = (1, -4) [/tex]
So, you have the equations
[tex] \frac{-3+x_T}{2} = 1,\qquad \frac{5+y_T}{2} = -4 [/tex]
Multply both equations by 2 to get
[tex] -3+x_T = 2,\qquad 5+y_T = -8 [/tex]
Move the constants to the right hand sides to get
[tex] x_T = 5,\qquad y_T = -13 [/tex]
