To find the distance between the two points \((2, 5)\) and \((-6, -3)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, the coordinates are:
- \(x_1 = 2\), \(y_1 = 5\)
- \(x_2 = -6\), \(y_2 = -3\)
Now, substituting these values into the distance formula:
\[ d = \sqrt{((-6) - 2)^2 + ((-3) - 5)^2} \]
Calculating the differences:
\[ d = \sqrt{(-8)^2 + (-8)^2} \]
Calculating the squares:
\[ d = \sqrt{64 + 64} \] \[ d = \sqrt{128} \]
Now we simplify \(\sqrt{128}\):
\[ \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2} \]
Now we can calculate \(8\sqrt{2}\):
Using \(\sqrt{2} \approx 1.414\):
\[ 8\sqrt{2} \approx 8 \times 1.414 \approx 11.312 \]
Finally, rounding to the nearest tenth:
\[ d \approx 11.3 \]
Therefore, the distance between the two points is approximately \(11.3\).