Final answer:
To find the coordinates of point S given the coordinates of point T and the midpoint of ST, we can use the midpoint formula. The formula states that the midpoint of a line segment is the average of the coordinates of its endpoints. Using this formula, we can solve for the coordinates of point S.
Step-by-step explanation:
To find the coordinates of point S, we can use the midpoint formula. The formula states that the midpoint of a line segment is the average of the coordinates of its endpoints. Since we know the coordinates of point T and the midpoint of ST, we can substitute these values into the formula to solve for the coordinates of point S.
Using the midpoint formula: (x₁ + x₂)/2 = x₃ and (y₁ + y₂)/2 = y₃, we can substitute the given values to get (6 + x₂)/2 = 6 and (-13 + y₂)/2 = -10. Solving these equations, we find that x₂ = 6 and y₂ = -7.
Therefore, the coordinates of point S are (6, -7).