If T is the midpoint of , 

SU find x.   

It seems like part of your question got cut off, but I can still guide you through the general problem involving midpoints. Here’s how we solve for \( x \) when \( T \) is the midpoint of segment \( SU \).

### Given Information:
- \( T \) is the midpoint of segment \( SU \).
- Let's assume the coordinates of \( S \) and \( U \) are given, or the lengths of segments \( ST \) and \( TU \) are expressed in terms of \( x \).

### The Midpoint Formula:
The midpoint formula for a segment connecting two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

If the coordinates of \( T \) are known, you can set up equations by equating the midpoint formula to the coordinates of \( T \) and solving for \( x \).

### Example Setup:
Let’s assume \( S \) and \( U \) are given as expressions of \( x \).

- \( S = (x_1, y_1) = (x - 3, 2) \)
- \( U = (x_2, y_2) = (3x + 1, 8) \)
  
If \( T \) is the midpoint, we set the midpoint equal to \( T \) and solve for \( x \).

### Solving for \( x \):
Equate the x-coordinates of \( T \):

\[
\frac{(x - 3) + (3x + 1)}{2} = T_x
\]

Solve for \( x \) by simplifying and isolating \( x \).

Would you like to clarify the coordinates or lengths, or should I go ahead with an example calculation?

Here are some related questions:
1. How does the midpoint affect the lengths of the segments?
2. If the midpoint is known, how do we find the endpoints?
3. Can the midpoint formula apply to three-dimensional space?
4. What happens if the midpoint divides the segment in a different ratio?
5. How would the formula change if only one endpoint is known?

**Tip:** Always ensure that you correctly apply the midpoint formula by averaging both the x- and y-coordinates of the endpoints.

Learn how to find the value of x when T is the midpoint of segment SU using the midpoint formula in coordinate geometry. This problem involves setting up equations and solving for x based on given coordinates of points S and U. Suitable for Grades 9-12.

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