To find the distance between two points on a coordinate plane, we use the distance formula:

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

From the graph, the two points are approximately:

• Point 1: $(2, -3)$
• Point 2: $(-3, -9)$

Step-by-step calculation:

1. Substitute the coordinates into the distance formula:

$d = \sqrt{((-3) - (2))^2 + ((-9) - (-3))^2}$

2. Simplify the expressions inside the parentheses:

$d = \sqrt{(-5)^2 + (-6)^2}$

3. Square the values:

$d = \sqrt{25 + 36}$

4. Add the results:

$d = \sqrt{61}$

Thus, the distance between the two points is $\sqrt{61}$, which is the simplest radical form.

Would you like more details on any step or further clarification?

5 related questions:

1. How can you derive the distance formula from the Pythagorean theorem?
2. What are other ways to find distances between points in different dimensions?
3. How would the distance change if one or both points were shifted along an axis?
4. Can the distance formula be applied in 3D, and how would it change?
5. What are some practical applications of the distance formula in real life?

Tip:

When applying the distance formula, always double-check the signs of your coordinates before squaring them to avoid errors.