To find the distance between the two points \((3, 6)\) and \((-1, 8)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1) = (3, 6)\) and \((x_2, y_2) = (-1, 8)\).
Now, substituting the coordinates into the formula:
\[ d = \sqrt{((-1) - 3)^2 + (8 - 6)^2} \]
Calculating inside the parentheses:
\[ d = \sqrt{(-4)^2 + (2)^2} \]
Calculating the squares:
\[ d = \sqrt{16 + 4} \]
Adding the results:
\[ d = \sqrt{20} \]
Now, simplifying \(\sqrt{20}\):
\[ d = \sqrt{4 \times 5} = 2\sqrt{5} \]
Using a calculator to approximate \( \sqrt{5} \approx 2.236\):
\[ d \approx 2 \times 2.236 = 4.472 \]
Rounding to the nearest tenth:
\[ d \approx 4.5 \]
Thus, the distance between the points \((3,6)\) and \((-1,8)\) is approximately 4.5.