Distance and Midpoint

The distance formula is given by: $$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$$ .

The midpoint is calculated using the formula: $$M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$$ .

Using the distance formula: $$d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ .

Using the distance formula: $$d = \sqrt{(1 - (-3))^2 + (2 - (-4))^2} = \sqrt{(1 + 3)^2 + (2 + 4)^2} = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13}$$ .

Using the distance formula: $$d = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ .

Using the distance formula: $$d = \sqrt{(2 - 2)^2 + (7 - 3)^2} = \sqrt{0 + 16} = \sqrt{16} = 4$$ .

Using the midpoint formula: $$M = \left(\frac{2 + 4}{2}, \frac{3 + 7}{2}\right) = (3, 5)$$ .

Using the midpoint formula: $$M = \left(\frac{-1 + 3}{2}, \frac{-2 + 4}{2}\right) = (1, 1)$$ .

Using the distance formula: $$d = \sqrt{(5 - 5)^2 + (1 - 5)^2} = \sqrt{0 + 16} = \sqrt{16} = 4$$ .

Using the distance formula: $$d = \sqrt{(2 - 6)^2 + (4 - 8)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}$$ .