Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

Looking at the x-axis, it can be said that every tick is equal to 2 from having 6 marks with 12 and -12 being the 6th marks on both ends. On the other hand, on y-axis, every tick is equal to 2 because of the 6 marks and 12 and -12 being the 6th marks.

The first point from right to left is 4 units to the left and 6 units above the origin. Thus, (-4, 6) = (x₁, y₁) .

The second point is 4 units to the right and 8 units above the origin. Thus, (4, -8) = (x₂, y₂) .

The length of the line segment is the distance between the points $(x_1,y_1)=(-4,6)\mathrm{and}(x_2,y_2)=(4,-8)$.

Using the distance formula the length d is

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{(y_2-y_2)}^2} \\ d=\sqrt{{\left(4-(-4)\right)}^2+{(-8-6)}^2} \\ d=\sqrt{{\left(8\right)}^2+{(-14)}^2} \\ d=\sqrt{64+196} \\ d=\sqrt{260} \\ d=2\sqrt{65} \end{gathered}$$

The length of line segment is$2\sqrt{65}$.