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The image presents a mathematical problem about finding the distance and midpoint between two points. It states:

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**Example 2**  
Find (a) the distance between, and (b) the midpoint of the line segment that joins the points \((-2, 1)\) and \((3, 4)\).

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Let's solve this step by step:

### (a) Distance between the points
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the distance formula:

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

Substitute the coordinates \((-2, 1)\) and \((3, 4)\):

\[
d = \sqrt{(3 - (-2))^2 + (4 - 1)^2} = \sqrt{(3 + 2)^2 + (4 - 1)^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}
\]

So, the distance is \(\sqrt{34} \approx 5.83\).

### (b) Midpoint of the segment
The midpoint \(M\) of the line segment joining the points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substitute the points:

\[
M = \left( \frac{-2 + 3}{2}, \frac{1 + 4}{2} \right) = \left( \frac{1}{2}, \frac{5}{2} \right) = \left( 0.5, 2.5 \right)
\]

Thus, the midpoint is \((0.5, 2.5)\).

### Summary:
- The distance between the points is \(\sqrt{34} \approx 5.83\).
- The midpoint is \((0.5, 2.5)\).

Would you like any further clarification or details? 

Here are five related questions for practice:
1. What is the distance between the points \((0, 0)\) and \((4, 3)\)?
2. Find the midpoint between \((1, -2)\) and \((7, 6)\).
3. How would you calculate the distance between points in 3D space?
4. What happens to the distance formula if both points are identical?
5. If the distance between two points is 10, what could the coordinates of the points be?

**Tip**: For accuracy, always check your work by squaring the differences carefully when using the distance formula.

Encuentre (a) la distancia entre, y (b) el punto medio del segmento de recta que une los puntos (-2, 1) y (3, 4).

Learn how to find the distance and midpoint between the points (-2, 1) and (3, 4) using coordinate geometry. Includes step-by-step explanations of the distance and midpoint formulas. Suitable for students in Grades 7-9.

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