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To solve for the coordinates of point \( S \), we use the formula for the midpoint between two points \( T(x_1, y_1) \) and \( S(x_2, y_2) \):

\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = (6, -7)
\]

We are given:
- Coordinates of \( T \): \( (0, 5) \)
- Midpoint \( M \): \( (6, -7) \)

Let's calculate the coordinates of point \( S(x_2, y_2) \).

### Step 1: Solve for \( x_2 \)
From the midpoint formula, we know:

\[
\frac{0 + x_2}{2} = 6
\]

Multiplying both sides by 2:

\[
0 + x_2 = 12 \quad \Rightarrow \quad x_2 = 12
\]

### Step 2: Solve for \( y_2 \)
Again, from the midpoint formula:

\[
\frac{5 + y_2}{2} = -7
\]

Multiplying both sides by 2:

\[
5 + y_2 = -14 \quad \Rightarrow \quad y_2 = -14 - 5 = -19
\]

### Final Answer:
The coordinates of point \( S \) are \( (12, -19) \).

Let me know if you'd like more details or have any questions. Here are 5 related questions you might find helpful:

1. How do you find the midpoint between two points?
2. What happens when both endpoints are unknown?
3. How do you calculate the distance between two points using coordinates?
4. How is the midpoint formula related to geometry in the coordinate plane?
5. What is the significance of finding the other endpoint in real-world applications?

**Tip**: The midpoint formula is useful for finding the center of line segments in both 2D and 3D geometry.

The coordinates of point T are (0, 5). The midpoint of ST is (6, -7). Find the coordinates of point S.

Solve for the coordinates of point S given that point T is (0, 5) and the midpoint of ST is (6, -7). This problem covers key concepts in coordinate geometry, including the use of the midpoint formula.

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