To find the distance between the two points $A$ and $B$, we can use the distance formula:

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

From the grid, let's identify the coordinates of points $A$ and $B$.

• Point $A$ appears to be at $(-2, 4)$
• Point $B$ appears to be at $(3, 1)$

Now, we substitute these coordinates into the distance formula:

$d = \sqrt{(3 - (-2))^2 + (1 - 4)^2}$ $d = \sqrt{(3 + 2)^2 + (-3)^2}$ $d = \sqrt{5^2 + (-3)^2}$ $d = \sqrt{25 + 9}$ $d = \sqrt{34} \approx 5.83 \, \text{units}$

Thus, the distance between points $A$ and $B$ is approximately 5.83 units.

Would you like further details, or do you have any questions?

Here are some related questions to explore:

1. How does the distance formula relate to the Pythagorean theorem?
2. How would the distance change if point $B$ were moved horizontally by 2 units?
3. Can the distance formula be used in 3D space? How?
4. What happens to the distance between two points if both coordinates are doubled?
5. How can you derive the distance formula from the equation of a circle?

Tip: Always make sure to use parentheses carefully in the distance formula to avoid errors when subtracting negative numbers.