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
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], then
[tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
* 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 = [tex](x_{1},y_{1})[/tex]
∵ The coordinates of point R are (-9 , 4)
∴ [tex]x_{1}=-9[/tex] and [tex]y_{1}=4[/tex]
∵ Point T = [tex](x_{2},y_{2})[/tex]
- By using the rule of the mid-point above find the coordinates
of point T
∴ [tex]2=\frac{-9+x_{2}}{2}[/tex]
- multiply both sides by 2
∴ [tex]4=-9+x_{2}[/tex]
- Add 9 to both sides
∴ [tex]x_{2}=13[/tex]
∴ [tex]-1=\frac{4+y_{2}}{2}[/tex]
- multiply both sides by 2
∴ [tex]-2=4+y_{2}[/tex]
- Subtract 4 from both sides
∴ [tex]y_{2}=-6[/tex]
∴ The coordinates of point T are (13 , -6)
