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Determine the coordinate of 𝐷, the midpoint of 𝐴𝐵.

To find the coordinates of point \( D \), the midpoint of line segment \( AB \), you can use the midpoint formula. The midpoint \( D(x, y) \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

Given the coordinates:
- \( A(2, 1) \)
- \( B(-4, -3) \)

We can plug these into the midpoint formula:

\[
D\left(\frac{2 + (-4)}{2}, \frac{1 + (-3)}{2}\right) = D\left(\frac{2 - 4}{2}, \frac{1 - 3}{2}\right) = D\left(\frac{-2}{2}, \frac{-2}{2}\right) = D(-1, -1)
\]

So, the coordinates of \( D \), the midpoint of \( AB \), are \( (-1, -1) \).

Would you like more details or have any questions? Here are some related questions:

1. How do you find the midpoint if the points are given in a 3D space?
2. What is the distance between point \( D \) and point \( C(1, -4) \)?
3. Can you find the equation of the line passing through points \( A \) and \( B \)?
4. What are the coordinates of the centroid of triangle \( ABC \)?
5. How would you find the area of triangle \( ABC \) using its vertices?

**Tip:** When working with geometric problems, always visualize the points on the coordinate plane to gain better insights into the problem.

Learn how to find the coordinates of point D, the midpoint of line segment AB with endpoints (2, 1) and (-4, -3). This problem involves using the midpoint formula in coordinate geometry. Suitable for students in Grades 9-12.

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