To find the length between the two points \((-2, -1)\) and \((2, 4)\), we can use the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
First, we identify our points:
- \(x_1 = -2\), \(y_1 = -1\)
- \(x_2 = 2\), \(y_2 = 4\)
Now, we calculate the differences in the coordinates:
\[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \]
\[ y_2 - y_1 = 4 - (-1) = 4 + 1 = 5 \]
Now we can substitute these values into the distance formula:
\[ d = \sqrt{(4)^2 + (5)^2} = \sqrt{16 + 25} = \sqrt{41} \]
Finally, we can approximate \(\sqrt{41}\).
Calculating \(\sqrt{41} \approx 6.403124237\).
Rounding to the nearest hundredth, the distance \(d\) is approximately:
\[ \boxed{6.40} \]