Find the distance between the points. Give an exact answer and an approximation to three decimal places. \( (-1,-6) \) and \( (-11,-11) \)

To find the distance between the points \((-1,-6)\) and \((-11,-11)\), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in our points: \[ d = \sqrt{((-11) - (-1))^2 + ((-11) - (-6))^2} \] \[ d = \sqrt{(-11 + 1)^2 + (-11 + 6)^2} \] \[ d = \sqrt{(-10)^2 + (-5)^2} = \sqrt{100 + 25} = \sqrt{125} = 5\sqrt{5} \] The exact answer is \(5\sqrt{5}\). To approximate this, we can calculate \(5 \times 2.236\) (since \(\sqrt{5} \approx 2.236\)): \[ 5\sqrt{5} \approx 5 \times 2.236 \approx 11.180 \] Thus, the distance between the points is \(5\sqrt{5}\) (exact) and approximately \(11.180\) (to three decimal places).