1. Problem: Find the distance between the points $A(3,4)$ and $B(7,1)$.\n\n2. Step 1: Use the distance formula between two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$: $$distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$\n\n3. Step 2: Substitute the values: $$distance = \sqrt{(7-3)^2 + (1-4)^2} = \sqrt{4^2 + (-3)^2}$$\n\n4. Step 3: Simplify: $$distance = \sqrt{16 + 9} = \sqrt{25} = 5$$\n\nAnswer: The distance between points $A$ and $B$ is 5 units.\n\n\n1. Problem: Find the midpoint of the segment joining points $C(-2,5)$ and $D(4,-3)$.\n\n2. Step 1: Use the midpoint formula for points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$: $$Midpoint = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$\n\n3. Step 2: Substitute the values: $$Midpoint = \left(\frac{-2 + 4}{2}, \frac{5 + (-3)}{2}\right) = \left(\frac{2}{2}, \frac{2}{2}\right)$$\n\n4. Step 3: Simplify: $$Midpoint = (1, 1)$$\n\nAnswer: The midpoint of segment $CD$ is at point $(1,1)$.\n\n\n1. Problem: Find the equation of the line passing through points $E(1,2)$ and $F(4,8)$.\n\n2. Step 1: Calculate the slope $m$ using: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$\n\n3. Step 2: Substitute the values: $$m = \frac{8 - 2}{4 - 1} = \frac{6}{3} = 2$$\n\n4. Step 3: Use point-slope form of a line $$y - y_1 = m(x - x_1)$$\n\n5. Step 4: Substitute slope and point $E(1,2)$: $$y - 2 = 2(x - 1)$$\n\n6. Step 5: Simplify: $$y - 2 = 2x - 2 \Rightarrow y = 2x$$\n\nAnswer: The equation of the line is $y = 2x$.