To calculate the distance between the two points shown on the graph in simplest radical form, we can use the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step 1: Identify the coordinates of the points.

From the graph:

• First point: $(-2, 4)$
• Second point: $(7, -8)$

Step 2: Apply the distance formula.

Substitute the coordinates into the formula:

$d = \sqrt{(7 - (-2))^2 + (-8 - 4)^2}$

Simplify the expressions: $d = \sqrt{(7 + 2)^2 + (-8 - 4)^2}$ $d = \sqrt{9^2 + (-12)^2}$ $d = \sqrt{81 + 144}$ $d = \sqrt{225}$

Step 3: Simplify the square root.

$d = 15$

Final Answer:

The distance between the two points is: $\boxed{15}$

Would you like further details or have any questions about this? Here are 5 related questions to explore:

1. How does the distance formula relate to the Pythagorean theorem?
2. What happens if the points are in 3D space—how does the formula change?
3. Can the distance between points ever be negative? Why or why not?
4. How can this formula be used to calculate the perimeter of polygons?
5. How do we find the midpoint of two points using a similar method?

Tip: Always double-check the coordinates you read from a graph to avoid errors in calculations.