91Ó°ÊÓ

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$2\sqrt{65}$.