To find the distance between the points \((2, 3)\) and \((-4, -9)\), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let's designate the points as follows:
- \( (x_1, y_1) = (2, 3) \)
- \( (x_2, y_2) = (-4, -9) \)
Substituting the coordinates into the formula:
\[ d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2} \] \[ d = \sqrt{(-6)^2 + (-12)^2} \] \[ d = \sqrt{36 + 144} \] \[ d = \sqrt{180} \] \[ d = \sqrt{36 \times 5} \] \[ d = 6\sqrt{5} \]
To get a decimal approximation:
\[ \sqrt{5} \approx 2.236 \] \[ d \approx 6 \times 2.236 \approx 13.416 \]
Rounding to the nearest hundredth:
\[ d \approx 13.42 \]
The distance between the points \((2, 3)\) and \((-4, -9)\) is approximately \(13.42\) units.