To find the distance between the two points \((3, -4)\) and \((9, -9)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Here, we have:
- \(x_1 = 3\)
- \(y_1 = -4\)
- \(x_2 = 9\)
- \(y_2 = -9\)
Now, substitute the values into the formula:
\[ d = \sqrt{(9 - 3)^2 + (-9 - (-4))^2} \]
Calculating the differences:
\[ d = \sqrt{(6)^2 + (-9 + 4)^2} \]
This simplifies to:
\[ d = \sqrt{(6)^2 + (-5)^2} \]
Now calculate the squares:
\[ d = \sqrt{36 + 25} \]
Adding the two values:
\[ d = \sqrt{61} \]
Now we can find the numerical value:
\[ d \approx 7.8102 \]
Rounding to the nearest tenth, we find:
\[ d \approx 7.8 \]
Thus, the distance between the two points is approximately 7.8 units.