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 1 because of the 6 marks and 6 and -6 being the 6th marks. The first point from right to left is 8 unit to the left and 4 units below the origin. Thus, (-8, -4) = (x₁, y₁) .

The second point is 2 units to the right and 3 units above the origin. Thus, (2, 3) = (x₂, y₂) .

The length of the line segment is the distance between the points $(x_1,y_1)=(-8,-4)\mathrm{and}(x_2,y_2)=(2,3)$.

Using the distance formula the length d is

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{(y_2-y_2)}^2} \\ d=\sqrt{{\left(2-(-8)\right)}^2+{(3-(-4\left)\right)}^2} \\ d=\sqrt{{10}^2+7^2} \\ d=\sqrt{100+49} \\ d=\sqrt{149} \end{gathered}$$

The length of line segment is$\sqrt{149}$.