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The problem asks to find the coordinates of the midpoint of the line segment \( EF \), where the coordinates of \( E \) are \( (-8, 5) \) and the coordinates of \( F \) are \( (12, 19) \).

To find the midpoint \( M \) of a line segment given its endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \), we use the midpoint formula:

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

Substituting the values for \( E(-8, 5) \) and \( F(12, 19) \):

\[
M = \left( \frac{-8 + 12}{2}, \frac{5 + 19}{2} \right)
\]

Now, let's calculate the coordinates:

\[
M = \left( \frac{4}{2}, \frac{24}{2} \right) = (2, 12)
\]

Thus, the coordinates of the midpoint are \( M(2, 12) \).

Would you like further details or have any questions?

### Related questions:
1. How do you calculate the length of a line segment given its endpoints?
2. What is the formula for finding the slope of a line?
3. How can you determine if two line segments are parallel?
4. What are the coordinates of the midpoint of the line segment joining \( (0, 0) \) and \( (6, 8) \)?
5. How do you find the equation of a line given two points?

### Tip:
Remember that the midpoint formula can be applied in 3D space as well by extending it to three coordinates: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \).

What are the coordinates of the midpoint of line segment EF, shown below?

Learn how to find the midpoint of a line segment EF with endpoints at (-8, 5) and (12, 19). This problem explores key concepts in coordinate geometry and uses the midpoint formula. Suitable for students in Grades 6-8.

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