Find the midpoint between (-2,4) and (5,-10).

To find the midpoint between the points \((-2, 4)\) and \((5, -10)\), use the midpoint formula:

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

Plugging in the coordinates:

- \(x_1 = -2\)
- \(y_1 = 4\)
- \(x_2 = 5\)
- \(y_2 = -10\)

Calculating the \(x\) coordinate of the midpoint:

\[
\frac{-2 + 5}{2} = \frac{3}{2} = 1.5
\]

Calculating the \(y\) coordinate of the midpoint:

\[
\frac{4 + (-10)}{2} = \frac{4 - 10}{2} = \frac{-6}{2} = -3
\]

Thus, the midpoint is:

\[
\left( 1.5, -3 \right)
\]

### Questions for Further Exploration:
1. What is the distance between the two points?
2. How would you find the midpoint of three points?
3. Can you explain how the midpoint formula is derived?
4. What are the coordinates of the midpoint if the points were in a different quadrant?
5. How does the midpoint relate to the line segment connecting the two points?

### Tip:
When calculating midpoints or distances, it can be helpful to sketch the points on a coordinate plane for better visualization.

Learn to calculate the midpoint between the points (-2, 4) and (5, -10) using the midpoint formula. This guide includes a step-by-step solution and related exploration questions. Suitable for students in Grades 6-8.

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