To find the distance 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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the values from our points:
- \(x_1 = -2\), \(y_1 = -1\)
- \(x_2 = 2\), \(y_2 = 4\)
Now, calculate the differences:
\[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \] \[ y_2 - y_1 = 4 - (-1) = 4 + 1 = 5 \]
Now substitute these differences back into the distance formula:
\[ d = \sqrt{(4)^2 + (5)^2} \] \[ d = \sqrt{16 + 25} \] \[ d = \sqrt{41} \]
Now, we need to round to the nearest hundredth:
\(\sqrt{41} \approx 6.4\) (using a calculator or estimating).
So, rounding to the nearest hundredth, the distance is approximately:
6.40.
From the options provided, the correct response is 6:40.