Answer:
The coordinates of point T are (13 , -6)
Step-by-step explanation:
* Lets explain how to solve the problem
- If point (x , y) is the mid point of a line whose end points are
and
, then
and ![y=\frac{y_{1}+y_{2}}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D)
* Lets solve the problem
∵ Point S is the mid point of segment RT
∴ S = (x , y)
∵ The coordinates of point S are (2 , -1)
∴ x = 2 and y = -1
∵ Point R = ![(x_{1},y_{1})](https://tex.z-dn.net/?f=%28x_%7B1%7D%2Cy_%7B1%7D%29)
∵ The coordinates of point R are (-9 , 4)
∴
and ![y_{1}=4](https://tex.z-dn.net/?f=y_%7B1%7D%3D4)
∵ Point T = ![(x_{2},y_{2})](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29)
- By using the rule of the mid-point above find the coordinates
of point T
∴ ![2=\frac{-9+x_{2}}{2}](https://tex.z-dn.net/?f=2%3D%5Cfrac%7B-9%2Bx_%7B2%7D%7D%7B2%7D)
- multiply both sides by 2
∴ ![4=-9+x_{2}](https://tex.z-dn.net/?f=4%3D-9%2Bx_%7B2%7D)
- Add 9 to both sides
∴ ![x_{2}=13](https://tex.z-dn.net/?f=x_%7B2%7D%3D13)
∴ ![-1=\frac{4+y_{2}}{2}](https://tex.z-dn.net/?f=-1%3D%5Cfrac%7B4%2By_%7B2%7D%7D%7B2%7D)
- multiply both sides by 2
∴ ![-2=4+y_{2}](https://tex.z-dn.net/?f=-2%3D4%2By_%7B2%7D)
- Subtract 4 from both sides
∴ ![y_{2}=-6](https://tex.z-dn.net/?f=y_%7B2%7D%3D-6)
∴ The coordinates of point T are (13 , -6)