To find the distance between the two points on the coordinate plane shown in the image, we use the distance formula, which is:

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

Let's identify the coordinates of the two points from the graph:

• The first point (near the origin) appears to be at $(-4, -2)$.
• The second point (above the x-axis) appears to be at $(2, 3)$.

Now, substitute these coordinates into the distance formula:

$d = \sqrt{(2 - (-4))^2 + (3 - (-2))^2}$

Simplify each term:

$d = \sqrt{(2 + 4)^2 + (3 + 2)^2}$

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

$d = \sqrt{36 + 25}$

$d = \sqrt{61}$

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

If you have any questions or need further clarification, feel free to ask!

Here are 5 related questions to explore further:

1. How would you find the midpoint between the two points?
2. What would the distance be if the points were on the same line parallel to the x-axis?
3. How do you calculate the distance between two points in 3D space?
4. What does the distance formula represent geometrically on the coordinate plane?
5. How would the distance formula change if we used polar coordinates?

Tip: When calculating distances, always ensure you've correctly identified the coordinates of the points to avoid mistakes.