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Let's break down the tasks from the image you've provided. The problems are divided into three sections: identifying quadrants, finding slopes, and determining midpoints.

### In which quadrant would you find each point? 
1. **(1, 2)**: **Quadrant I** (both coordinates are positive)
2. **(-4, 3)**: **Quadrant II** (x is negative, y is positive)
3. **(2, -3)**: **Quadrant IV** (x is positive, y is negative)
4. **(-2, -4)**: **Quadrant III** (both coordinates are negative)
5. **(-4, -5)**: **Quadrant III** (both coordinates are negative)
6. **(-1, -3)**: **Quadrant III** (both coordinates are negative)

### Find the slope of each line.
- **Line in Figure 1**: To find the slope, use the formula \(\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}\).
  - Points: (1, 2) and (-4, -3)
  - Slope \(= \frac{-3 - 2}{-4 - 1} = \frac{-5}{-5} = 1\)

- **Line in Figure 2**: 
  - Points: (-3, -3) and (3, 1)
  - Slope \(= \frac{1 - (-3)}{3 - (-3)} = \frac{4}{6} = \frac{2}{3}\)

- **Line in Figure 3**: 
  - Points: (-2, -1) and (1, 3)
  - Slope \(= \frac{3 - (-1)}{1 - (-2)} = \frac{4}{3}\)

### Find the slope of the line containing these points:
10. **(-3, 4) and (2, -6)**:
    - Slope \(= \frac{-6 - 4}{2 - (-3)} = \frac{-10}{5} = -2\)

11. **(25, 40) and (100, 55)**:
    - Slope \(= \frac{55 - 40}{100 - 25} = \frac{15}{75} = \frac{1}{5}\)

### Find the midpoint of the segment with the given endpoints.
12. **(-4, -4) and (2, 6)**:
    - Midpoint \(= \left(\frac{-4 + 2}{2}, \frac{-4 + 6}{2}\right) = \left(-1, 1\right)\)

13. **(3, 13) and (-7, -8)**:
    - Midpoint \(= \left(\frac{3 + (-7)}{2}, \frac{13 + (-8)}{2}\right) = \left(-2, 2.5\right)\)

14. **(-1, -1) and (0, -3)**:
    - Midpoint \(= \left(\frac{-1 + 0}{2}, \frac{-1 + (-3)}{2}\right) = \left(-0.5, -2\right)\)

15. **(3, 1) and (2, -6)**:
    - Midpoint \(= \left(\frac{3 + 2}{2}, \frac{1 + (-6)}{2}\right) = \left(2.5, -2.5\right)\)

Would you like a more detailed explanation of any of these answers or have any other questions?

Here are five related questions to further practice:

1. Which quadrant does the point (5, -7) lie in?
2. What is the slope of the line that passes through (4, -2) and (-2, -4)?
3. Find the midpoint of the line segment between (7, 9) and (-3, -1).
4. How do you determine the quadrant for a point on a coordinate plane?
5. What is the slope of a line parallel to the line containing (1, 2) and (4, 8)?

**Tip:** When finding the midpoint, you're essentially averaging the x-coordinates and the y-coordinates of the endpoints.

In which quadrant would you find each point? Find the slope of each line. Find the midpoint of the segment with the given endpoints.

Learn how to determine the quadrant for a point, find the slope of a line, and calculate the midpoint of a segment with detailed step-by-step solutions. This problem covers key geometry concepts, including slope and midpoint formulas. Suitable for students in Grades 7-9.

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