To find the coordinates of point \( D \), which is the midpoint of the hypotenuse of \( \triangle ABC \), we need to identify the two endpoints of the hypotenuse and then use the midpoint formula.

### Hypotenuse of \( \triangle ABC \)
In a right triangle, the hypotenuse is the side opposite the right angle. Based on the diagram, it seems the hypotenuse is the line connecting points \( A(3, 6) \) and \( B(7, -3) \).

### Midpoint Formula
The midpoint \( D(x, y) \) of a line segment connecting two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

### Calculation
Let’s calculate the coordinates of point \( D \) using the points \( A(3, 6) \) and \( B(7, -3) \).

\[
D_x = \frac{3 + 7}{2} = \frac{10}{2} = 5
\]
\[
D_y = \frac{6 + (-3)}{2} = \frac{6 - 3}{2} = \frac{3}{2} = 1.5
\]

Thus, the coordinates of point \( D \) are \( (5, 1.5) \).

Would you like to proceed with the next question or delve deeper into this result?

Here are 5 related questions to explore:
1. How do you verify that line \( AB \) is indeed the hypotenuse?
2. What is the length of the hypotenuse \( AB \)?
3. How do you find the equation of the line passing through point \( D \)?
4. Can you calculate the slope of line \( AB \)?
5. How does the midpoint relate to the circumcenter of a right triangle?

**Tip:** The midpoint of the hypotenuse in a right triangle is also the circumcenter, meaning it's equidistant from all three vertices.

Learn how to find the midpoint of the hypotenuse of triangle ABC with a detailed step-by-step solution. This problem covers key concepts in geometry and coordinate geometry, including the use of the midpoint formula and the midpoint theorem. Suitable for students in Grades 9-12.

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