To find the distance between the points \( (2, 3) \) and \( (-4, -9) \), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, let \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (-4, -9) \).
Now, substitute the values into the formula:
\[ d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2} \]
Calculate the differences:
\[ d = \sqrt{(-6)^2 + (-12)^2} \]
Now calculate the squares:
\[ d = \sqrt{36 + 144} \]
Add them together:
\[ d = \sqrt{180} \]
Finally, simplify \( \sqrt{180} \):
\[ d = \sqrt{36 \times 5} = 6\sqrt{5} \]
So, the distance between the two points is:
\[ 6\sqrt{5} \]