If one endpoint of a line segment is at \( (-1, -3) \) and the other endpoint is at \( (4, 5) \), determine the length of the line segment.

To find the length of the line segment between the points \((-1, -3)\) and \((4, 5)\), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, \((x_1, y_1) = (-1, -3)\) and \((x_2, y_2) = (4, 5)\). Plugging in these values, we get: \[ d = \sqrt{(4 - (-1))^2 + (5 - (-3))^2} \] This simplifies to: \[ d = \sqrt{(4 + 1)^2 + (5 + 3)^2} = \sqrt{(5)^2 + (8)^2} \] Calculating the squares: \[ d = \sqrt{25 + 64} = \sqrt{89} \] Thus, the length of the line segment is \( \sqrt{89} \).