Q. 48 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The length of line segment is $\sqrt{205}$.

Step 1. Given information.

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

Step 2. locate the coordinates of end points of line segment.

Looking at the x-axis, it can be said that every tick is equal to 1 from having 6 marks with 6 and -6 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 on the origin and 6 units above the origin. Thus, (0, 6) = (x₁, y₁) .

The second point is 3 units to the right and 8 units below the origin. Thus, (3, -8) = (x₂, y₂) .

Step 3. Substitute the values in the distance formula.

The length of the line segment is the distance between the points $(x_1,y_1)=(0,6) \mathrm{and} (x_2,y_2)=(3,-8)$.

Using the distance formula the length d is

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{(y_2-y_2)}^2} \\ d=\sqrt{{\left(3-0\right)}^2+{(-8-6)}^2} \\ d=\sqrt{3^2+{(-14)}^2} \\ d=\sqrt{9+196} \\ d=\sqrt{205} \end{gathered}$$

Step 4. Conclusion.

The length of line segment is $\sqrt{205}$.