Final Answer
The coordinates of point S are (6, -19). y-coordinate of S = 2 * midpoint's y-coordinate - T's y-coordinate = 2 * (-9) - (-14) = -18 + 14 = -4. Hence, the coordinates of point S are (6, -4).
Explanation:
Given that the coordinates of point T are (6, -14) and the midpoint between points S and T is (6, -9), we can find the coordinates of point S. The midpoint formula states that the midpoint between two points (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
In this case, if the midpoint between S and T is (6, -9), the x-coordinate remains the same as point T, which is 6. To find the y-coordinate of point S, we need to calculate the difference between the y-coordinate of point T (-14) and double the y-coordinate of the midpoint (-9).
Thus, y-coordinate of S = 2 * midpoint's y-coordinate - T's y-coordinate = 2 * (-9) - (-14) = -18 + 14 = -4. Hence, the coordinates of point S are (6, -4).