https://file.aiquickdraw.com/mathbot/file/1726704524364httmwvem.jpg

The problem on your screen asks to:

1. **Find the midpoint** of points \( S(-2, 4) \) and \( T(3, 9) \).
2. **Find the distance** between these points, rounding to the nearest tenth.

Let's break it down step-by-step:

### 1. Midpoint Formula:
The midpoint \( M \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using:

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

For \( S(-2, 4) \) and \( T(3, 9) \):

\[
M = \left( \frac{-2 + 3}{2}, \frac{4 + 9}{2} \right) = \left( \frac{1}{2}, \frac{13}{2} \right) = (0.5, 6.5)
\]

So, the midpoint \( M \) is **(0.5, 6.5)**.

### 2. Distance Formula:
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

For \( S(-2, 4) \) and \( T(3, 9) \):

\[
d = \sqrt{(3 - (-2))^2 + (9 - 4)^2} = \sqrt{(3 + 2)^2 + (5)^2} = \sqrt{(5)^2 + (5)^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.1
\]

So, the distance between \( S \) and \( T \) is approximately **7.1 units**.

Would you like more details or have any questions?

### 5 Related Questions:
1. How do you find the midpoint of three points in a triangle?
2. What is the distance formula in three-dimensional space?
3. How can you determine if two points are collinear?
4. Can the midpoint be used to find the center of a circle given two endpoints of a diameter?
5. What are the applications of the distance formula in real-world problems?

### Tip:
Remember, the midpoint formula gives the exact middle point between two points, while the distance formula calculates the straight-line distance.

Find the coordinates of the midpoint of S(-2, 4) and T(3, 9). Then find the distance between S and T. Round the distance to the nearest tenth.

Learn how to find the midpoint and distance between points S(-2, 4) and T(3, 9) using the midpoint and distance formulas. This problem is suitable for students in Grades 7-10, covering key concepts in geometry.

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