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In this image, the problem involves finding the midpoint and distance between two points, \( S(5, 5) \) and \( T(7, -2) \).

### Solution Steps:

#### 1. Midpoint Formula:
The formula for the midpoint \( M \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

For points \( S(5, 5) \) and \( T(7, -2) \):

\[
M = \left( \frac{5 + 7}{2}, \frac{5 + (-2)}{2} \right) = \left( \frac{12}{2}, \frac{3}{2} \right) = (6, 1.5)
\]

So, the midpoint is \( (6, 1.5) \).

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

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

For points \( S(5, 5) \) and \( T(7, -2) \):

\[
d = \sqrt{(7 - 5)^2 + (-2 - 5)^2} = \sqrt{(2)^2 + (-7)^2} = \sqrt{4 + 49} = \sqrt{53} \approx 7.28
\]

Thus, the distance between \( S \) and \( T \) is approximately 7.28 units.

Would you like any further clarification or details?

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Here are five related questions for practice:
1. What is the midpoint between the points \( A(2, 3) \) and \( B(8, -4) \)?
2. Find the distance between the points \( C(-1, 2) \) and \( D(3, 6) \).
3. If the midpoint between points \( P(1, y) \) and \( Q(5, 7) \) is \( (3, 4) \), what is the value of \( y \)?
4. What is the formula for finding the midpoint between two points in three-dimensional space?
5. How does the distance formula relate to the Pythagorean theorem?

**Tip:** The midpoint formula is useful not only for geometry problems but also for finding the center of line segments in coordinate geometry.

Find the midpoint and the distance between the points S(5, 5) and T(7, -2).

Learn how to calculate the midpoint and distance between two points, S(5, 5) and T(7, -2), using key coordinate geometry concepts. This problem demonstrates the application of the midpoint and distance formulas, suitable for students in Grades 8-10.

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