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.