The coordinates of the point S are (2, -17). Using the midpoint of ST, the required coordinates of S are calculated.
The midpoint of a line A(x1, y1) and B(x2, y2) is
M(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
The given line segment is ST. Its coordinates are S(x1, y1) and T(0,3).
It is given that the coordinates of the midpoint M of the given line segment are (1, -7)
Then,
M(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
On substituting,
(1, -7) = [tex](\frac{x1+0}{2},\frac{y1+3}{2})[/tex]
On equating,
1 = x1/2
⇒ x1 = 2
and
-7 = (y1+3)/2
⇒ y1 + 3 = -14
⇒ y1 = -14 - 3 = - 17
Thus, the coordinates of the point S are (2, -17).
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