Let the co-ordinates of the point S be (x, y).
Let the co-ordinates of the point T be (a, b) (given values)
Let the midpoint of ST be O.
Then, O is (5, - 8)
Also, the midpoint of ST can be calculated as follows:
O is [tex](\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2} )[/tex]
= [tex](\frac{x+a}{2}, \frac{y+b}{2} )[/tex]
Therefore,
[tex](\frac{x+a}{2} , \frac{y+b}{2} ) = (5, - 8)[/tex]
x = 10 - a and y = -16 - b
Hence the co-ordinates of S are (10 - a, -16 - b).
