To find the length between the two points \((-2, -1)\) and \((2, 4)\), we can use the distance formula, which is derived from the Pythagorean theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, the coordinates are:
- \((x_1, y_1) = (-2, -1)\)
- \((x_2, y_2) = (2, 4)\)
Now, substitute the values into the distance formula:
\[ d = \sqrt{(2 - (-2))^2 + (4 - (-1))^2} \]
Calculate the differences:
\[ d = \sqrt{(2 + 2)^2 + (4 + 1)^2} \] \[ d = \sqrt{(4)^2 + (5)^2} \] \[ d = \sqrt{16 + 25} \] \[ d = \sqrt{41} \]
Now, let's round \(\sqrt{41}\). The square root of 41 is approximately 6.403124237...
Rounding this to the nearest hundredth gives:
\[ d \approx 6.40 \]
Thus, the length between the two points, rounded to the nearest hundredth, is \(6.40\).
The correct response is: 6:40