Ask AI: What is the distance between the points (1,–1) and (–5,9)?

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a Cartesian plane, you can use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Given the points \((1, -1)\) and \((-5, 9)\), we can substitute \(x_1 = 1\), \(y_1 = -1\), \(x_2 = -5\), and \(y_2 = 9\) into the formula: \[ \text{Distance} = \sqrt{((-5) - 1)^2 + (9 - (-1))^2} \] First, simplify inside the parentheses: \[ \text{Distance} = \sqrt{(-6)^2 + (10)^2} \] Next, calculate the squares of these numbers: \[ \text{Distance} = \sqrt{36 + 100} \] Finally, add the values and take the square root: \[ \text{Distance} = \sqrt{136} \] \[ \text{Distance} = \sqrt{4 \times 34} \] \[ \text{Distance} = 2\sqrt{34} \] So, the distance between the points \((1, -1)\) and \((-5, 9)\) is \(2\sqrt{34}\) units.