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The midpoint *M* of *ST* has coordinates (5, 0). Point *S* has coordinates (2, 0). Find the coordinates of point *T*.

*Write the coordinates as decimals or integers.*

To find the coordinates of point \( T \), we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( S(x_1, y_1) \) and \( T(x_2, y_2) \) is given by:

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

We know:
- The midpoint \( M \) is \( (5, 0) \).
- The coordinates of point \( S \) are \( (2, 0) \).

Let the coordinates of point \( T \) be \( (x_2, y_2) \). Using the midpoint formula:

\[
\left( \frac{2 + x_2}{2}, \frac{0 + y_2}{2} \right) = (5, 0)
\]

This gives two equations:

1. \( \frac{2 + x_2}{2} = 5 \)
2. \( \frac{y_2}{2} = 0 \)

### Solving for \( x_2 \):
\[
\frac{2 + x_2}{2} = 5
\]
Multiply both sides by 2:
\[
2 + x_2 = 10
\]
Subtract 2 from both sides:
\[
x_2 = 8
\]

### Solving for \( y_2 \):
\[
\frac{y_2}{2} = 0
\]
Multiply both sides by 2:
\[
y_2 = 0
\]

Thus, the coordinates of point \( T \) are \( (8, 0) \).

### Final Answer:
The coordinates of point \( T \) are \( \boxed{(8, 0)} \).

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. If the midpoint \( M \) is \( (4, 3) \) and \( S = (1, 2) \), find the coordinates of \( T \).
2. What are the coordinates of \( T \) if \( M = (3, 5) \) and \( S = (2, 4) \)?
3. How does the midpoint formula change in 3D space if \( M = (x, y, z) \)?
4. Find the distance between points \( S = (1, 1) \) and \( T = (4, 5) \).
5. If \( S = (-2, 3) \) and \( T = (6, -1) \), what is the midpoint of \( ST \)?

**Tip:** Always double-check by plugging the values back into the original formula to verify your result!

The midpoint M of ST has coordinates (5, 0). Point S has coordinates (2, 0). Find the coordinates of point T. Write the coordinates as decimals or integers.

Learn how to find the coordinates of point T when the midpoint M of ST is (5, 0) and point S is (2, 0). This step-by-step solution covers key concepts in coordinate geometry, including the midpoint formula and solving linear equations. Suitable for students in Grades 6-8.

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