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 ![T = (5,-13)](https://tex.z-dn.net/?f=%20T%20%3D%20%285%2C-13%29%20)
If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.
We have
and
. The midpoint is computed as
![A = \left( \frac{-3+x_T}{2},\frac{5+y_T}{2} \right) = (1, -4)](https://tex.z-dn.net/?f=%20A%20%3D%20%5Cleft%28%20%5Cfrac%7B-3%2Bx_T%7D%7B2%7D%2C%5Cfrac%7B5%2By_T%7D%7B2%7D%20%5Cright%29%20%3D%20%281%2C%20-4%29%20)
So, you have the equations
![\frac{-3+x_T}{2} = 1,\qquad \frac{5+y_T}{2} = -4](https://tex.z-dn.net/?f=%20%5Cfrac%7B-3%2Bx_T%7D%7B2%7D%20%3D%201%2C%5Cqquad%20%5Cfrac%7B5%2By_T%7D%7B2%7D%20%3D%20-4%20)
Multply both equations by 2 to get
![-3+x_T = 2,\qquad 5+y_T = -8](https://tex.z-dn.net/?f=%20-3%2Bx_T%20%3D%202%2C%5Cqquad%205%2By_T%20%3D%20-8%20)
Move the constants to the right hand sides to get
![x_T = 5,\qquad y_T = -13](https://tex.z-dn.net/?f=%20x_T%20%3D%205%2C%5Cqquad%20y_T%20%3D%20-13%20)