To find the distance between the points \((2, 3)\) and \((-4, -9)\), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (-4, -9)\).
Now, let's calculate the difference in the x-coordinates and the y-coordinates:
\[ x_2 - x_1 = -4 - 2 = -6 \] \[ y_2 - y_1 = -9 - 3 = -12 \]
Next, we square these differences:
\[ (-6)^2 = 36 \] \[ (-12)^2 = 144 \]
Now, we can plug these values into the distance formula:
\[ d = \sqrt{36 + 144} = \sqrt{180} \]
Now, we simplify \(\sqrt{180}\):
\[ \sqrt{180} = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5} \]
Next, we calculate \(6\sqrt{5}\) to the nearest hundredth. We know that:
\[ \sqrt{5} \approx 2.236 \] So,
\[ 6\sqrt{5} \approx 6 \times 2.236 \approx 13.416 \]
Finally, rounding this to the nearest hundredth, we get:
\[ \boxed{13.42} \]
Thus, the distance between the points \((2, 3)\) and \((-4, -9)\) is approximately \(13.42\).