Answer:
[tex](10,-7)[/tex]
Step-by-step explanation:
If two points are given as [tex](x_{1},y_{1})[/tex] (point 1) and [tex](x_{2},y_{2})[/tex] (point 2), then the midpoint of these 2 points are given by the formula:
Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
Using R as point 1 , S as point 2, and T as midpoint, we can substitute in the formula and get 2 equations shown below:
[tex]4=\frac{-2+x_{2}}{2}[/tex] * This is equation 1 from which we can find [tex]x_{2}[/tex]
[tex]-2=\frac{3+y_{2}}{2}[/tex] * This is equation 2 from which we can find [tex]y_{2}[/tex]
Solving equation 1:
[tex]4=\frac{-2+x_{2}}{2}\\8=-2+x_{2}\\8+2=x_{2}\\x_{2}=10[/tex]
Solving equation 2:
[tex]-2=\frac{3+y_{2}}{2}\\-4=3+y_{2}\\-4-3=y_{2}\\y_{2}=-7[/tex]
Hence the coordinates of point S is [tex](10,-7)[/tex]
