Distance and Midpoint

The distance formula is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

The midpoint formula is given by: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ .

Congruent segments are segments that have the same length.

AB is equal to BC, meaning AB = BC.

Using the distance formula: $$d = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{16 + 9} = 5$$ .

The midpoint divides the line segment into two equal parts.

Midpoint M = $$\left(\frac{2 + 4}{2}, \frac{3 + 7}{2}\right) = (3, 5)$$ .

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

To bisect a line segment means to divide it into two equal parts.

Distance = $$d = \sqrt{(5 - 1)^2 + (6 - 2)^2} = \sqrt{16 + 16} = 4\sqrt{2}$$ .