To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In your case, the points are \((2, 3)\) and \((-4, -9)\). Here, we have:
- \(x_1 = 2\)
- \(y_1 = 3\)
- \(x_2 = -4\)
- \(y_2 = -9\)
Now, let's substitute these values into the distance formula:
\[ d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2} \]
Calculating the differences:
\[ d = \sqrt{(-6)^2 + (-12)^2} \]
Now, calculate the squares:
\[ d = \sqrt{36 + 144} \]
Adding these together:
\[ d = \sqrt{180} \]
Now, we can simplify \(\sqrt{180}\):
\[ \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5} \]
Now, calculating \(6\sqrt{5}\) using \(\sqrt{5} \approx 2.236\):
\[ 6 \times 2.236 \approx 13.416 \]
Rounding to the nearest hundredth, the distance is:
\[ \boxed{13.42} \]