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You are asking to find the **midpoint** and **distance** between the points \((-5,6)\) and \((8,12)\).

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

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

Substitute the given points \((-5, 6)\) and \((8, 12)\) into the formula:

\[
\text{Midpoint} = \left(\frac{-5 + 8}{2}, \frac{6 + 12}{2}\right) = \left(\frac{3}{2}, \frac{18}{2}\right) = \left(1.5, 9\right)
\]

So, the **midpoint** is \((1.5, 9)\).

### 2. **Distance Formula**:
The formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substitute the given points \((-5, 6)\) and \((8, 12)\) into the formula:

\[
\text{Distance} = \sqrt{(8 - (-5))^2 + (12 - 6)^2} = \sqrt{(8 + 5)^2 + (12 - 6)^2} = \sqrt{13^2 + 6^2} = \sqrt{169 + 36} = \sqrt{205}
\]

\[
\text{Distance} \approx 14.32
\]

So, the **distance** between the two points is approximately **14.32** units.

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Would you like more details or have any other questions? Here are some related problems you could explore:

1. How do you find the slope of the line between two points?
2. What is the equation of the line that passes through these two points?
3. Can you find the midpoint of three or more points?
4. How do you find the distance between two points in three-dimensional space?
5. What is the perimeter of a triangle formed by these two points and the origin?

**Tip**: When calculating the distance between points, ensure to square the differences before summing them, as small errors in this step can lead to incorrect results!

Midpoint and Distance of (-5, 6) and (8, 12)

Learn how to calculate the midpoint and distance between the points (-5, 6) and (8, 12). This example demonstrates key concepts in coordinate geometry, including the midpoint formula and distance formula. Suitable for students in Grades 9-10.

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