The given points are $(-2, 4)$ and $(1, 1)$. Let's calculate the slope, distance, and the midpoint of the line segment connecting these two points.

1. Slope ($m$) Calculation

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the given points: $m = \frac{1 - 4}{1 - (-2)} = \frac{-3}{3} = -1$ Slope: $-1$

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2. Distance ($d$) Calculation

The formula for the distance is: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substitute the given points: $d = \sqrt{(1 - (-2))^2 + (1 - 4)^2} = \sqrt{(3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}$ Distance: $3\sqrt{2}$ (approximately $4.24$)

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3. Midpoint Calculation

The formula for the midpoint is: $\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ Substitute the given points: $\text{Midpoint} = \left( \frac{-2 + 1}{2}, \frac{4 + 1}{2} \right) = \left( \frac{-1}{2}, \frac{5}{2} \right)$ Midpoint: $\left( -\frac{1}{2}, \frac{5}{2} \right)$

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Final Results:

1. Slope: $-1$
2. Distance: $3\sqrt{2}$
3. Midpoint: $\left( -\frac{1}{2}, \frac{5}{2} \right)$

Would you like further details or graphical representation?

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Here are some follow-up questions for exploration:

1. What is the equation of the line passing through these points?
2. How does changing one coordinate affect the slope and distance?
3. Can the points form a right triangle with the origin? Why or why not?
4. What is the equation of a circle with these two points as endpoints of a diameter?
5. How would you graph these points and calculate the results visually?

Tip: Always visualize the points on a graph to better understand relationships like slope and distance.