To solve this problem, we need to determine the distance of the line given in the image. It appears to involve a diagonal line segment between two clearly defined points on a coordinate grid.

Step-by-Step Solution:

1. Identify the Points:

   • From the graph, the line appears to connect two points:
     • Point 1: $(-5, 5)$
     • Point 2: $(5, -5)$

2. Use the Distance Formula: The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

   Substituting the coordinates of the points: $x_1 = -5, \, y_1 = 5, \, x_2 = 5, \, y_2 = -5$

3. Perform the Calculations: Substitute the values into the formula: $d = \sqrt{(5 - (-5))^2 + ((-5) - 5)^2}$ Simplify: $d = \sqrt{(5 + 5)^2 + (-5 - 5)^2}$ $d = \sqrt{(10)^2 + (-10)^2}$ $d = \sqrt{100 + 100}$ $d = \sqrt{200}$ Simplify further: $d = 10\sqrt{2}$

4. Final Answer: The distance of the line is: $d = 10\sqrt{2} \, \text{units}.$

Would you like further details or an explanation about any specific step?

Related Questions:

1. What is the formula for finding the slope of a line given two points?
2. How can you verify the coordinates of points from a graph?
3. What is the significance of the diagonal distance in a square or grid?
4. Can the distance formula be used in 3D space? If so, how is it extended?
5. How does the Pythagorean theorem relate to the distance formula?

Tip:

Always simplify square roots, when possible, to make your final answer clearer. For example, $\sqrt{200} = 10\sqrt{2}$.